ABSTRACT

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

chapter Chapter 1|85 pages

Banach function lattices

chapter Chapter 2|22 pages

Fundamental facts in functional analysis

chapter Chapter 3|19 pages

Polynomials and harmonic functions

chapter Chapter 4|91 pages

Various operators in Lebesgue spaces

chapter Chapter 5|26 pages

BMO spaces and Morrey—Campanato spaces

chapter Chapter 6|45 pages

General metric measure spaces

chapter Chapter 7|49 pages

Weighted Lebesgue spaces

chapter Chapter 8|19 pages

Approximations in Morrey spaces

chapter Chapter 9|46 pages

Predual of Morrey spaces

chapter Chapter 10|31 pages

Linear and sublinear operators in Morrey spaces