Martingale Hardy Spaces and their Applications in Fourier Analysis
Weisz, Ferenc.
Martingale Hardy Spaces and their Applications in Fourier Analysis [electronic resource] / by Ferenc Weisz. - VIII, 224 p. online resource. - Lecture Notes in Mathematics, 1568 0075-8434 ; . - Lecture Notes in Mathematics, 1568 .
Preliminaries and notations -- One-parameter Martingale Hardy spaces -- Two-Parameter Martingale Hardy spaces -- Tree martingales -- Real interpolation -- Inequalities for Vilenkin-fourier coefficients.
This book deals with the theory of one- and two-parameter martingale Hardy spaces and their use in Fourier analysis, and gives a summary of the latest results in this field. A method that can be applied for both one- and two-parameter cases, the so-called atomic decomposition method, is improved and provides a new and common construction of the theory of one- and two-parameter martingale Hardy spaces. A new proof of Carleson's convergence result using martingale methods for Fourier series is given with martingale methods. The book is accessible to readers familiar with the fundamentals of probability theory and analysis. It is intended for researchers and graduate students interested in martingale theory, Fourier analysis and in the relation between them.
9783540482956
10.1007/BFb0073448 doi
Distribution (Probability theory.
Global analysis (Mathematics).
Probability Theory and Stochastic Processes.
Analysis.
QA273.A1-274.9 QA274-274.9
519.2
Martingale Hardy Spaces and their Applications in Fourier Analysis [electronic resource] / by Ferenc Weisz. - VIII, 224 p. online resource. - Lecture Notes in Mathematics, 1568 0075-8434 ; . - Lecture Notes in Mathematics, 1568 .
Preliminaries and notations -- One-parameter Martingale Hardy spaces -- Two-Parameter Martingale Hardy spaces -- Tree martingales -- Real interpolation -- Inequalities for Vilenkin-fourier coefficients.
This book deals with the theory of one- and two-parameter martingale Hardy spaces and their use in Fourier analysis, and gives a summary of the latest results in this field. A method that can be applied for both one- and two-parameter cases, the so-called atomic decomposition method, is improved and provides a new and common construction of the theory of one- and two-parameter martingale Hardy spaces. A new proof of Carleson's convergence result using martingale methods for Fourier series is given with martingale methods. The book is accessible to readers familiar with the fundamentals of probability theory and analysis. It is intended for researchers and graduate students interested in martingale theory, Fourier analysis and in the relation between them.
9783540482956
10.1007/BFb0073448 doi
Distribution (Probability theory.
Global analysis (Mathematics).
Probability Theory and Stochastic Processes.
Analysis.
QA273.A1-274.9 QA274-274.9
519.2