This comprehensive exploration of a metric approach to some relevant problems and techniques in analysis focuses on examining spaces of homogeneous type. Both the structural and analytical problems under consideration reflect very active areas of current research. The exposition, motivated by examples and details of which many cannot be found elsewhere in book form, unfolds systematically in three parts, starting from such preliminaries as the basic structures of quasi-metric spaces, the homogeneity property and measure theory.
This comprehensive exploration of a metric approach to some relevant problems and techniques in analysis focuses on examining spaces of homogeneous type. Both the structural and analytical problems under consideration reflect very active areas of current research. The exposition, motivated by examples and details of which many cannot be found elsewhere in book form, unfolds systematically in three parts, starting from such preliminaries as the basic structures of quasi-metric spaces, the homogeneity property and measure theory.
Part I: POINT SPACES Quasi-Metric Spaces The Weak Homogeneity Property on Quasi-Metric Spaces Spaces of Homogeneous Type Examples Part II: FUNCTION SPACES The Hardy--Littlewood Maximal Function and the Differentiation Theorem Lipschitz Functions The Space L^2 Hardy and John--Birenberg Spaces BMO (f) Spaces Harnack Inequalities and Hölder--Lipschitz Regularity of Functions Besov--Taibleson and Triebel--Lizorkin Spaces Part III: OPERATORS Weighted Norm Inequalities or the Hardy--Littlewood Maximal Operator Electrostatic Potentials and Singular Integrals of Calderón--Zygmund Type Singular Integrals Unconditional Haar Bases for L^p (1
Part I: POINT SPACES Quasi-Metric Spaces The Weak Homogeneity Property on Quasi-Metric Spaces Spaces of Homogeneous Type Examples Part II: FUNCTION SPACES The Hardy--Littlewood Maximal Function and the Differentiation Theorem Lipschitz Functions The Space L^2 Hardy and John--Birenberg Spaces BMO (f) Spaces Harnack Inequalities and Hölder--Lipschitz Regularity of Functions Besov--Taibleson and Triebel--Lizorkin Spaces Part III: OPERATORS Weighted Norm Inequalities or the Hardy--Littlewood Maximal Operator Electrostatic Potentials and Singular Integrals of Calderón--Zygmund Type Singular Integrals Unconditional Haar Bases for L^p (1
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