Morrey spaces were introduced by Charles Morrey to investigate the local behaviour of solutions to second order elliptic partial dierential equations. The technique is very useful in many areas in mathematics, in particular in harmonic analysis, potential theory, partial dierential equations and mathematical physics.
Across two volumes, the authors of Morrey Spaces: Introduction and Applications to Integral Operators and PDEs 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 readers understanding
The Open Access version of this book, available at http://www.taylorfrancis.com, has been made available under a Creative Commons [ Attribution-Non Commercial-No Derivatives (CC BY-NC-ND)] 4.0 license.
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.
Yoshihiro Sawano is associate professor in Department of Mathematics and Information Sciences at Tokyo Metropolitan University. Before joining Tokyo Metropolitan University in 2012, he served as assistant professor at Kyoto University from November 2009 to March 2012. Yoshihiro received PhD from The University of Tokyo in the year 2006. His research interests include harmonic analysis and the reproducing kernel Hilbert spaces.
Giuseppe Di Fazio is Full Professor at University of Catania. He received his PhD in Mathematics in 1992 from University of Catania. He has worked as visiting professor at many universities around the world including Temple University, MSRI at Berkeley, University of Kyoto, Universita Autonoma de Madrid, ITB at Bandung Indonesia and Tokyo Metropolitan University. His research interests is focused on regularity problems for elliptic PDEs and boundedness properties of integral operators acting on Morrey spaces.
Denny Ivanal Hakim is a lecturer at Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology since 2014. He obtained his PhD in Mathematics at Tokyo Metropolitan University in 2018 under supervision of Professor Yoshihiro Sawano and his bachelors and asters from Bandung Institute of Technology. His research interests include boundedness of integral operators in Morrey spaces, interpolation of Morrey spaces, and other function spaces, and also regularity theory of elliptic partial differential equations. He has authored or co-authored more than 20 research articles.
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