Bounded and Compact Integral Operators:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
2002
|
| Schriftenreihe: | Mathematics and Its Applications
543 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The monograph presents some of the authors' recent and original results concerning boundedness and compactness problems in Banach function spaces both for classical operators and integral transforms defined, generally speaking, on nonhomogeneous spaces. Itfocuses onintegral operators naturally arising in boundary value problems for PDE, the spectral theory of differential operators, continuum and quantum mechanics, stochastic processes etc. The book may be considered as a systematic and detailed analysis of a large class of specific integral operators from the boundedness and compactness point of view. A characteristic feature of the monograph is that most of the statements proved here have the form of criteria. These criteria enable us, for example, togive var ious explicit examples of pairs of weighted Banach function spaces governing boundedness/compactness of a wide class of integral operators. The book has two main parts. The first part, consisting of Chapters 1-5, covers theinvestigation ofclassical operators: Hardy-type transforms, fractional integrals, potentials and maximal functions. Our main goal is to give a complete description of those Banach function spaces in which the above-mentioned operators act boundedly (com pactly). When a given operator is not bounded (compact), for example in some Lebesgue space, we look for weighted spaces where boundedness (compact ness) holds. We develop the ideas and the techniques for the derivation of appropriate conditions, in terms of weights, which are equivalent to bounded ness (compactness) |
| Beschreibung: | 1 Online-Ressource (XVI, 643 p) |
| ISBN: | 9789401599221 9789048160181 |
| DOI: | 10.1007/978-94-015-9922-1 |
Internformat
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| 490 | 0 | |a Mathematics and Its Applications |v 543 | |
| 500 | |a The monograph presents some of the authors' recent and original results concerning boundedness and compactness problems in Banach function spaces both for classical operators and integral transforms defined, generally speaking, on nonhomogeneous spaces. Itfocuses onintegral operators naturally arising in boundary value problems for PDE, the spectral theory of differential operators, continuum and quantum mechanics, stochastic processes etc. The book may be considered as a systematic and detailed analysis of a large class of specific integral operators from the boundedness and compactness point of view. A characteristic feature of the monograph is that most of the statements proved here have the form of criteria. These criteria enable us, for example, togive var ious explicit examples of pairs of weighted Banach function spaces governing boundedness/compactness of a wide class of integral operators. The book has two main parts. The first part, consisting of Chapters 1-5, covers theinvestigation ofclassical operators: Hardy-type transforms, fractional integrals, potentials and maximal functions. Our main goal is to give a complete description of those Banach function spaces in which the above-mentioned operators act boundedly (com pactly). When a given operator is not bounded (compact), for example in some Lebesgue space, we look for weighted spaces where boundedness (compact ness) holds. We develop the ideas and the techniques for the derivation of appropriate conditions, in terms of weights, which are equivalent to bounded ness (compactness) | ||
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Datensatz im Suchindex
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| indexdate | 2024-07-10T01:21:15Z |
| institution | BVB |
| isbn | 9789401599221 9789048160181 |
| language | English |
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| spelling | Edmunds, David E. Verfasser aut Bounded and Compact Integral Operators by David E. Edmunds, Vakhtang Kokilashvili, Alexander Meskhi Dordrecht Springer Netherlands 2002 1 Online-Ressource (XVI, 643 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 543 The monograph presents some of the authors' recent and original results concerning boundedness and compactness problems in Banach function spaces both for classical operators and integral transforms defined, generally speaking, on nonhomogeneous spaces. Itfocuses onintegral operators naturally arising in boundary value problems for PDE, the spectral theory of differential operators, continuum and quantum mechanics, stochastic processes etc. The book may be considered as a systematic and detailed analysis of a large class of specific integral operators from the boundedness and compactness point of view. A characteristic feature of the monograph is that most of the statements proved here have the form of criteria. These criteria enable us, for example, togive var ious explicit examples of pairs of weighted Banach function spaces governing boundedness/compactness of a wide class of integral operators. The book has two main parts. The first part, consisting of Chapters 1-5, covers theinvestigation ofclassical operators: Hardy-type transforms, fractional integrals, potentials and maximal functions. Our main goal is to give a complete description of those Banach function spaces in which the above-mentioned operators act boundedly (com pactly). When a given operator is not bounded (compact), for example in some Lebesgue space, we look for weighted spaces where boundedness (compact ness) holds. We develop the ideas and the techniques for the derivation of appropriate conditions, in terms of weights, which are equivalent to bounded ness (compactness) Mathematics Harmonic analysis Fourier analysis Integral Transforms Operator theory Potential theory (Mathematics) Potential Theory Fourier Analysis Abstract Harmonic Analysis Integral Transforms, Operational Calculus Operator Theory Mathematik Operatortheorie (DE-588)4075665-8 gnd rswk-swf Integraloperator (DE-588)4131247-8 gnd rswk-swf Integraloperator (DE-588)4131247-8 s Operatortheorie (DE-588)4075665-8 s 1\p DE-604 Kokilashvili, Vakhtang Sonstige oth Meskhi, Alexander Sonstige oth https://doi.org/10.1007/978-94-015-9922-1 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Edmunds, David E. Bounded and Compact Integral Operators Mathematics Harmonic analysis Fourier analysis Integral Transforms Operator theory Potential theory (Mathematics) Potential Theory Fourier Analysis Abstract Harmonic Analysis Integral Transforms, Operational Calculus Operator Theory Mathematik Operatortheorie (DE-588)4075665-8 gnd Integraloperator (DE-588)4131247-8 gnd |
| subject_GND | (DE-588)4075665-8 (DE-588)4131247-8 |
| title | Bounded and Compact Integral Operators |
| title_auth | Bounded and Compact Integral Operators |
| title_exact_search | Bounded and Compact Integral Operators |
| title_full | Bounded and Compact Integral Operators by David E. Edmunds, Vakhtang Kokilashvili, Alexander Meskhi |
| title_fullStr | Bounded and Compact Integral Operators by David E. Edmunds, Vakhtang Kokilashvili, Alexander Meskhi |
| title_full_unstemmed | Bounded and Compact Integral Operators by David E. Edmunds, Vakhtang Kokilashvili, Alexander Meskhi |
| title_short | Bounded and Compact Integral Operators |
| title_sort | bounded and compact integral operators |
| topic | Mathematics Harmonic analysis Fourier analysis Integral Transforms Operator theory Potential theory (Mathematics) Potential Theory Fourier Analysis Abstract Harmonic Analysis Integral Transforms, Operational Calculus Operator Theory Mathematik Operatortheorie (DE-588)4075665-8 gnd Integraloperator (DE-588)4131247-8 gnd |
| topic_facet | Mathematics Harmonic analysis Fourier analysis Integral Transforms Operator theory Potential theory (Mathematics) Potential Theory Fourier Analysis Abstract Harmonic Analysis Integral Transforms, Operational Calculus Operator Theory Mathematik Operatortheorie Integraloperator |
| url | https://doi.org/10.1007/978-94-015-9922-1 |
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