Introduction to Hp spaces: with two appendices by V. P. Havin
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
1998
|
| Edition: | Second edition, corrected and augmented |
| Series: | Cambridge Tracts in Mathematics
115 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 287 Seiten graph. Darst. |
| ISBN: | 0521455219 |
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| 245 | 1 | 0 | |a Introduction to Hp spaces |b with two appendices by V. P. Havin |c Paul Koosis, McGill University in Montreal |
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Record in the Search Index
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| adam_text | PAUL KOOSIS MCGILL UNIVERSITY IN MONTREAL INTRODUCTION TO H P SPACES
SECOND EDITION, CORRECTED AND AUGMENTED WITH TWO APPENDICES BY V. P.
HAVIN ST. PETERSBURG (LENINGRAD) STATE AND MCGILL UNIVERSITIES CAMBRIDGE
UNIVERSITY PRESS CONTENTS PREFACE TO THE SECOND EDITION XI PREFACE TO
THE FIRST EDITION XIII I FUNCTIONS HARMONIC IN Z 1. RUDIMENTS 1 A
POWER SERIES REPRESENTATION 1 B POISSON S FORMULA - 2 C POISSON
REPRESENTATION OF HARMONIC FUNCTIONS BELONGING TO VARIOUS CLASSES 3 D
BOUNDARY BEHAVIOUR 5 1 INTEGRABILITY PROPERTIES OF HARMONIC FUNCTIONS
GIVEN BY POISSON S FORMULA 5 2 ELEMENTARY STUDY OF BOUNDARY BEHAVIOUR 1
3 DEEPER STUDY OF BOUNDARY BEHAVIOUR. NON-TANGENTIAL BOUNDARY VALUES AND
FATOU S THEOREM 10 PROBLEM 1 14 -~ E THE HARMONIC CONJUGATE 1 6 1
FORMULA FOR THE HARMONIC CONJUGATE 17 2 BEHAVIOUR OF HARMONIC CONJUGATE
NEAR AN ARC WHERE THE ORIGINAL BOUNDARY DATA FUNCTION HAS A CONTINUOUS
DERIVATIVE 18 PROBLEM 2 18 3 RADIAL BOUNDARY BEHAVIOUR OF HARMONIC
CONJUGATE NEAR POINTS OF ORIGINAL BOUNDARY DATA FUNCTION S LEBESGUE SET
19 4 EXISTENCE OF F (6) FOR F IN LI. DISCUSSION 21 5 EXISTENCE OFF(9)
REALLY DUE TO CANCELLATION. EXAMPLE 25 II THEOREM OF THE BROTHERS RIESZ.
INTRODUCTION TO THE SPACE HI 28 A THE F. AND M. RIESZ THEOREM 28
CONTENTS 1 ORIGINAL PROOF 28 2 MODERN HELSON AND LOWDENSLAGER PROOF 31 B
DEFINITION AND BASIC PROPERTIES OF H 34 1 POIS~SON REPRESENTATION FOR
FUNCTIONS IN H 34 2 L CONVERGENCE TO BOUNDARY DATA FUNCTION 35 3
CAUCHY SFORMULA 35 C DIGRESSION ON CONFORMAL MAPPING THEORY 35 1
CARATHEODORY S THEOREM ON CONTINUITY OF THE CONFORMAL MAPPING FUNCTION
UP TO A JORDAN CURVE BOUNDARY 36 2 LINDELOF S THEOREM ON THE BEHAVIOUR
OF CONFORMAL MAPPING FUNCTION NEAR A POINT OF TANGENCY OF THE BOUNDARY
40 3 WHEN THE BOUNDARY CURVE HAS A CONTINUOUSLY TURNING TANGENT 46 D
DOMAINS BOUNDED BY RECTIFIABLE JORDAN CURVES 52 1 DERIVATIVE OF
CONFORMAL MAPPING FUNCTION IS IN H 53 2 IMAGE OF A SET OF MEASURE ZERO
ON UNIT CIRCUMFERENCE 53 3 TAYLOR SERIES FOR THE CONFORMAL MAPPING
FUNCTION IS ABSOLUTELY CONVERGENT UP TO THE UNIT CIRCUMFERENCE 54
PROBLEM 3 56 III ELEMENTARY BOUNDARY BEHAVIOUR THEORY FOR ANALYTIC
FUNCTIONS 57 A A.E. EXISTENCE OF FINITE NON-TANGENTIAL BOUNDARY VALUES
57 B UNIQUENESS THEOREMS FOR H FUNCTIONS 57 C MORE EXISTENCE THEOREMS
FOR BOUNDARY VALUES 58 1 FUNCTIONS WITH POSITIVE REAL PART 58 2
EXISTENCE OFF(9)FOR F IN L 58 D PRIVALOV S UNIQUENESS THEOREM 59 1
PRIVALOV S ICE-CREAM CONE CONSTRUCTION 59 2 USE OF EGOROFF S THEOREM 6 1
3 PROOF OF PRIVALOV S THEOREM 62 E GENERALIZATIONS OF THE SCHWARZ
REFLECTION PRINCIPLE 63 1 SCHWARZ REFLECTION ACROSS AN ARC OF UNIT
CIRCLE FOR H FUNCTIONS 63 2 A THEOREM OF CARLEMAN 64 PROBLEM 4 64 IV
APPLICATION OF JENSEN S FORMULA. FACTORIZATION INTO A PRODUCT OF INNER
AND OUTER FUNCTIONS . 65 A BLASCHKE PRODUCTS. * 65 1 CRITERION FOR
CONVERGENCE 65 2 BOUNDARY VALUE IS ALMOST EVERYWHERE OF MODULUS 1 66
CONTENTS B FACTORIZING OUT BLASCHKE PRODUCTS 67 1 POSSIBILITY OF FORMING
A BLASCHKE PRODUCT HAVING SAME ZEROS AS A GIVEN FUNCTION ANALYTIC IN
UNIT CIRCLE 67 2~THE CLASS H P , 0 P CO. FACTORIZATION 68 C
FUNCTIONS IN H P , 0 P CO. 70 1 BOUNDARY DATA FUNCTION. NORM 70 2
CONVERGENCE IN MEAN TO THE BOUNDARY DATA FUNCTION. THIRD PROOF OF THE F.
AND M. RIESZ THEOREM 71 3 SMIRNOV S THEOREM 74 D INNER AND OUTER FACTORS
14 1 LEMMA ON ABSOLUTE CONTINUITY 74 2 |LOG|F(RE E )|| HAS BOUNDED
MEANS IF OG + F{RE I0 ) DOES 75 3 EXPRESSION OF AN ANALYTIC FUNCTION
IN TERMS OF ITS REAL PART 75 4 FACTORIZATION INTO INNER AND OUTER
FACTORS 76 E BEURLING S THEOREM 78 1 APPROXIMATION BY POLYNOMIALS 78 2
GENERALIZATION OF SMIRNOV S THEOREM 79 3 BEURLING S THEOREM IN H P 79 F
INVARIANT SUBSPACES 81 PROBLEM 5 , 83 G THE SPACE H X . FROSTMAN S
THEOREM ON THE UNIFORM APPROXIMATION OF INNER FUNCTIONS BY BLASCHKE
PRODUCTS 83 NORM INEQUALITIES FOR HARMONIC CONJUGATION 87 A REVIEW.
HILBERT TRANSFORMS OF LI FUNCTIONS 87 B HILBERT TRANSFORMS OF L P
FUNCTIONS, 1 P OO 88 1 AN IDENTITY 88 2 RIESZ THEOREM THAT F
BELONGS TO L P FOR F IN L P , 1 P OO 88 C F(6)FOR F IN L X 92 1
DEFINITION OF M/,(A). KOLMOGOROV S THEOREM 92 2 SECOND PROOF OF RIESZ
THEOREM ABOUT F FOR F IN L P BASED ON KOLMOGOROV S THEOREM AND
MARCINKIEWICZ INTERPOLATION 94 3 ZYGMUND S LLOGL THEOREM 4 CONVERSE OF
ZYGMUND S LLOGL THEOREM FOR POSITIVE F 96 5 ANOTHER THEOREM OF
KOLMOGOROV 98 D F{6) FOR BOUNDED OR CONTINUOUS AND PERIODIC F(D) 99 1
INTEGRABILITY OF EXP X F 99 2 CASE OF CONTINUOUS PERIODIC F 100 E
LIPSCHITZ CLASSES 100 CONTENTS F RETURN TO CONFORMAL MAPPING 101 VI H P
SPACES FOR THE UPPER HALF PLANE 10 6 A POISSON S FORMULA FOR THE HALF
PLANE 106 B BOUNDARY BEHAVIOUR 109 C THE H P SPACES FOR 3Z 0 112 D
RIESZ THEOREMS FOR THE HILBERT TRANSFORM 111 E FOURIER TRANSFORMS. THE
PALEY-WIENER THEOREM 130 F TITCHMARSH S CONVOLUTION THEOREM 135 PROBLEM
6 138 VII DUALITY FOR H P SPACES 140 A H P SPACES AND THEIR DUALS.
SARASON S THEOREM 140 1 VARIOUS SPACES AND THEIR DUALS. TABLES 140 2
APPROXIMATION BY H P FUNCTIONS. DUALITY METHOD OF HAVINSON AND OF
ROGOSINSKI AND SHAPIRO 143 3 SARASON S THEOREM ON NORM CLOSURE OF^ + H^
148 B ELEMENTS OF CONSTANT MODULUS IN COSETS OF LAO/H^. MARSHALL S
THEOREM 150 1 A RESULT OF ADAMIAN, AROV AND KREIN 150 2 MARSHALL S
THEOREM. UNIT SPHERE OF H M THE NORM-CLOSED CONVEX HULL OF BLASCHKE
PRODUCTS 15 2 C SZEGO S THEOREM 158 D THE HELSON-SZEGO THEOREM 163
PROBLEM 7 169 VIII APPLICATION OF THE HARDY-LITTLEWOOD MAXIMAL FUNCTION
170 A USE OF THE DISTRIBUTION FUNCTION 170 B THE HARDY-LITTLEWOOD
MAXIMAL FUNCTION 172 1 THEOREM OF HARDY AND LITTLEWOOD PROVED BY
RIESZ CONSTRUCTION 172 2 NORM INEQUALITIES FOR THE HARDY-LITTLEWOOD
MAXIMAL FUNCTION F M 174 3 CRITERION FOR F M TO BE INTEGRABLE ON SETS OF
FINITE MEASURE. STEIN S THEOREM 175 C APPLICATION TO FUNCTIONS ANALYTIC
OR HARMONIC IN THE UPPER HALF PLANE, OR IN UNIT CIRCLE 111 1 ESTIMATE OF
POISSON S INTEGRAL IN TERMS OF F M 111 2 THE NON-TANGENTIAL MAXIMAL
FUNCTION F (X), *OO X OO 178 3 THE NON-TANGENTIAL MAXIMAL FUNCTION
F (6), *N 9 N 180 4 THE MAXIMAL HILBERT TRANSFORM 181 D MAXIMAL
FUNCTION CHARACTERIZATION OF VIHI 181 CONTENTS 1 THEOREM OF BURKHOLDER,
GUNDY AND SILVER STEIN 182 2 CHARACTERIZATION OFHH IN TERMS OF THE
RADIAL MAXIMAL FUNCTION 185 3 DISCUSSION 187 E ATOMIC DECOMPOSITION IN
9LIF I 188 1 DISCUSSION O/9U/I(3Z 0) 188 2 CONSIDERATION OF3IH ( Z
1) 194 F CARLESON MEASURES 197 PROBLEM 8 199 IX INTERPOLATION 200 A
NECESSARY CONDITIONS 200 1 UNIFORMITY LEMMA 200 2 IL/I^N (L Z N ~ Z
K IVN * ZFCL) LUST FEE BOUNDED BELOW 201 B CARLESON S THEOREM 201 1
COMPUTATIONAL LEMMA 201 2 4 CARLESON MEASURE 202 3 PROOF OF CARLESON S
THEOREM 205 C WEIGHTED INTERPOLATION BY FUNCTIONS IN H P . THEOREM OF
SHIELDS AND SHAPIRO 207 D RELATIONS BETWEEN SOME CONDITIONS ON SEQUENCES
{Z N } 209 E INTERPOLATION BY BOUNDED HARMONIC FUNCTIONS. GARNETT S
THEOREM 211 PROBLEM 9 214 X FUNCTIONS OF BOUNDED MEAN OSCILLATION 215 A
DUAL OF 91^(0) 215 1 AN IDENTITY 215 2 REAL LINEAR FUNCTIONALS ON FFI(0)
216 B INTRODUCTION OF BMO 217 1 DEFINITION OF BMO 217 2 IF 4 AND P ARE
BOUNDED, + Y IS IN BMO 218 C GARSIA S NORM 221 1 DEFINITION O/ 2 TWO
SIMPLE INEQUALITIES FOR YX{ 221 3 WHERE WE ARE HEADING 223 D
COMPUTATIONS BASED ON GREEN S THEOREM . 224 1 SOME IDENTITIES 224 2 P.
STEIN S EXPRESSION OF THE H NORM AS A DOUBLE INTEGRAL 225 CONTENTS 3
VARIOUS WAYS OF EXPRESSING THE FACT THAT F(9) GENERATES A LINEAR
FUNCTIONAL ON WH^O) 225 E FEFFERMAN S THEOREM WITH THE GARSIA NORM 227 1
USE-OF SCHWARZ INEQUALITY 228 2 A MEASURE TO BE PROVED CARLESON 228 3
MAIN LEMMA 229 4 FEFFERMAN S THEOREM WITH 9T(.F) 234 F FEFFERMAN S
THEOREM WITH THE BMO NORM 235 1 THEOREM OF NIRENBERG AND JOHN 235 2
EQUIVALENCE OF BMO AND GARSIA NORMS 238 3 FEFFERMAN S THEOREM 240 G
ALTERNATIVE PROOF, BASED ON THE ATOMIC DECOMPOSITION IN JJHI 241 H
REPRESENTATION OF BMO FUNCTIONS IN TERMS OF RADIALLY BOUNDED MEASURES *
243 1 RADIALLY BOUNDED MEASURES. THEY GENERATE LINEAR FUNCTIONALS ON
9?HI(0) 243 2 ALL LINEAR FUNCTIONALS ON 3{H (Q) ARE GENERATED BY
RADIALLY BOUNDED MEASURES 246 PROBLEM 10 251 XI WOLFF S PROOF OF THE
CORONA THEOREM 252 A HOMOMORPHISMS OF H X AND MAXIMAL IDEALS 252 B THE
D-EQUATION 255 C PROOF OF THE CORONA THEOREM 258 APPENDICES BY V.P.
HAVIN APPENDIX I. JONES INTERPOLATION FORMULA 263 JL THE FORMULA 263 2
DISCUSSION 266 APPENDIX II. WEAK COMPLETENESS OF THE SPACE L /H (Q) 271
1 NOTION OF WEAK COMPLETENESS 111 2 GENERAL RESULT 272 3 VERIFICATION OF
PROPERTIES I-IV FOR H M 276 POSTSCRIPT 278 BIBLIOGRAPHY 279 INDEX 286
|
| any_adam_object | 1 |
| author | Koosis, Paul 1929- |
| author_GND | (DE-588)14232101X (DE-588)140937579 |
| author_facet | Koosis, Paul 1929- |
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| bvnumber | BV013298931 |
| classification_rvk | SK 700 SK 750 |
| classification_tum | MAT 150f |
| ctrlnum | (OCoLC)633170002 (DE-599)BVBBV013298931 |
| discipline | Mathematik |
| edition | Second edition, corrected and augmented |
| format | Book |
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| id | DE-604.BV013298931 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:43:21Z |
| institution | BVB |
| isbn | 0521455219 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009066588 |
| oclc_num | 633170002 |
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| physical | XIV, 287 Seiten graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | Cambridge Tracts in Mathematics |
| series2 | Cambridge Tracts in Mathematics |
| spelling | Koosis, Paul 1929- Verfasser (DE-588)14232101X aut Introduction to Hp spaces with two appendices by V. P. Havin Paul Koosis, McGill University in Montreal Second edition, corrected and augmented Cambridge Cambridge University Press 1998 XIV, 287 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge Tracts in Mathematics 115 Hp-Raum (DE-588)4160706-5 gnd rswk-swf Beweis (DE-588)4132532-1 gnd rswk-swf Corona-Theorem (DE-588)4760365-3 gnd rswk-swf Corona-Theorem (DE-588)4760365-3 s Beweis (DE-588)4132532-1 s DE-604 Hp-Raum (DE-588)4160706-5 s Chavin, Viktor P. 1933-2015 Sonstige (DE-588)140937579 oth Cambridge Tracts in Mathematics 115 (DE-604)BV000000001 115 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009066588&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Koosis, Paul 1929- Introduction to Hp spaces with two appendices by V. P. Havin Cambridge Tracts in Mathematics Hp-Raum (DE-588)4160706-5 gnd Beweis (DE-588)4132532-1 gnd Corona-Theorem (DE-588)4760365-3 gnd |
| subject_GND | (DE-588)4160706-5 (DE-588)4132532-1 (DE-588)4760365-3 |
| title | Introduction to Hp spaces with two appendices by V. P. Havin |
| title_auth | Introduction to Hp spaces with two appendices by V. P. Havin |
| title_exact_search | Introduction to Hp spaces with two appendices by V. P. Havin |
| title_full | Introduction to Hp spaces with two appendices by V. P. Havin Paul Koosis, McGill University in Montreal |
| title_fullStr | Introduction to Hp spaces with two appendices by V. P. Havin Paul Koosis, McGill University in Montreal |
| title_full_unstemmed | Introduction to Hp spaces with two appendices by V. P. Havin Paul Koosis, McGill University in Montreal |
| title_short | Introduction to Hp spaces |
| title_sort | introduction to hp spaces with two appendices by v p havin |
| title_sub | with two appendices by V. P. Havin |
| topic | Hp-Raum (DE-588)4160706-5 gnd Beweis (DE-588)4132532-1 gnd Corona-Theorem (DE-588)4760365-3 gnd |
| topic_facet | Hp-Raum Beweis Corona-Theorem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009066588&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000001 |
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