Morrey spaces : introduction and applications to integral operators and PDE's
著者
書誌事項
Morrey spaces : introduction and applications to integral operators and PDE's
（Monographs and research notes in mathematics）（A Chapman & Hall book）
C&H/CRC Press, c2020
- v. 1 : hardback
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注記
Includes bibliographical references (p. 441-474) and indexes
収録内容
- Banach function lattices
- Fundamental facts in functional analysis
- Polynomials and harmonic functions
- Various operators in Lebesgue spaces
- BMO spaces and Morrey-Campanato spaces
- BMO spaces and Morrey-Campanato spaces
- General metric measure spaces
- Weighted Lebesgue spaces
- Approximations in Morrey spaces
- Predual of Morrey spaces
- Linear and sublinear operators in Morrey spaces
内容説明・目次
内容説明
Morrey spaces were introduced by Charles Morrey to investigate the local behaviour of solutions to second order elliptic partial differential equations. The technique is very useful in many areas in mathematics, in particular in harmonic analysis, potential theory, partial differential equations and mathematical physics.
Across two volumes, the authors of Morrey Spaces: Introduction and Applications to Integral Operators and PDE's discuss the current state of art and perspectives of developments of this theory of Morrey spaces, with the emphasis in Volume I focused mainly on harmonic analysis.
Features
Provides a 'from-scratch' overview of the topic readable by anyone with an understanding of integration theory
Suitable for graduate students, masters course students, and researchers in PDE's or Geometry
Replete with exercises and examples to aid the reader's understanding
目次
1. Banach function lattices. 2. Fundamental facts in functional analysis. 3. Polynomials and harmonic functions. 4. Various operators in Lebesgue spaces. 5. BMO spaces and Morrey-Campanato spaces. 6. General metric measure spaces. 7. Weighted Lebesgue spaces. 8. Approximations in Morrey spaces. 9. Predual of Morrey spaces. 10. Linear and sublinear operators in Morrey spaces. Bibliography. Index.
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