Yoshihiro Sawano, Giuseppe Di Fazio, Denny Ivanal Hakim
Chapman and Hall/CRC
June 8, 2020 Forthcoming
Reference - 928 Pages
ISBN 9780367459178 - CAT# 357246
Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics
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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 focus on harmonic analysis in volume I and generalizations and interpolation of Morrey spaces in volume II.
Chapters in Volume I
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.
Chapters in Volume II
11. Multilinear operators and Morrey spaces. 12. Generalized Morrey/Morrey-Campanato spaces. 13. Generalized Orlicz-Morrey spaces. 14. Morrey spaces over metric measure spaces. 15. Weighted Morrey spaces. 16. Morrey-type spaces. 17. Pointwise product. 18. Real interpolation of Morrey spaces. 19. Complex interpolation of Morrey spaces. Bibliography. Index.