Geometric harmonic analysis. II, Function spaces measuring size and smoothness on rough sets / Dorina Mitrea, Irina Mitrea, Marius Mitrea.

This monograph is part of a larger program, materializing in five volumes, whose principal aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic...

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Bibliographic Details
Main Authors: Mitrea, Dorina, 1965- (Author), Mitrea, Irina (Author), Mitrea, Marius (Author)
Format: eBook
Published: Cham : Springer, 2022.
Series:Developments in mathematics ; v. 73.
Online Access:Click for online access
Table of Contents:
  • 1 Preliminary Functional Analytic Matters
  • 2 Abstract Fredholm Theory
  • 3 Functions of Vanishing Mean Oscillations and Vanishing Hlder Moduli
  • 4 Hardy Spaces on Ahlfors Regular Sets
  • 5 Banach Function Spaces, Extrapolation, and Orlicz Spaces
  • 6 Morrey-Campanato Spaces, Morrey Spaces, and Their Pre-Duals on Ahlfors Regular Sets
  • 7 Besov and Triebel-Lizorkin Spaces on Ahlfors Regular Sets
  • 8 Boundary Traces from Weighted Sobolev Spaces into Besov Spaces
  • 9 Besov and Triebel-Lizorkin Spaces in Open Sets
  • 10 Strong and Weak Normal Boundary Traces of Vector Fields in Hardy and Morrey Spaces
  • 11 Sobolev Spaces on the Geometric Measure Theoretic Boundary of Sets of Locally Finite Perimeter
  • A. Terms and Notation Used in Volume II. References
  • Index.