Dyadic Harmonic Analysis and Weighted Inequalities: The Sparse Revolution

AbstractMixed norm inequalities for directional operators are closely related to the boundedness problems of several important operators in harmonic analysis. In this paper we prove weighted inequalities for some one-dimensional one-sided maximal functions. Then by applying these results, we establish mixed norm inequalities for directional maximal operators which are defined from these one-dimensional maximal functions. We also estimate the constants in these inequalities.

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Weighted Inequalities and Dyadic Harmonic Analysis

Excursions in Harmonic Analysis, Volume 2 ◽

10.1007/978-0-8176-8379-5_15 ◽

2012 ◽

pp. 281-306 ◽

Cited By ~ 3

Author(s):

María Cristina Pereyra

Keyword(s):

Harmonic Analysis ◽

Weighted Inequalities

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Harmonic Analysis and Representation Theory for Groups Acting on Homogenous Trees

10.1017/cbo9780511662324 ◽

1991 ◽

Cited By ~ 36

Author(s):

Alessandro Figá-Talamanca ◽

Claudio Nebbia

Keyword(s):

Representation Theory ◽

Harmonic Analysis

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Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

10.1017/cbo9781107279087 ◽

2009 ◽

Author(s):

Tullio Ceccherini-Silberstein ◽

Fabio Scarabotti ◽

Filippo Tolli

Keyword(s):

Representation Theory ◽

Harmonic Analysis ◽

Finite Groups ◽

Wreath Products

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Classical and Multilinear Harmonic Analysis

10.1017/cbo9781139410397 ◽

2009 ◽

Author(s):

Camil Muscalu ◽

Wilhelm Schlag

Keyword(s):

Harmonic Analysis

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TRANSFORMS, DIFFERENTIAL SUBORDINATIONS AND A p -WEIGHTED INEQUALITIES FOR BANACH-SPACE-VALUED REGULAR MARTINGALES

Acta Mathematica Scientia ◽

10.1016/s0252-9602(18)30204-2 ◽

1993 ◽

Vol 13 (2) ◽

pp. 180-187

Author(s):

Peide Liu ◽

Youliang Hou

Keyword(s):

Banach Space ◽

Weighted Inequalities ◽

Differential Subordinations

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AN HARMONIC ANALYSIS FOR OPERATORS IN THE CASE OF A LOCALLY COMPACT ABELIAN GROUP: F. AND M. RIESZ THEOREMS

Acta Mathematica Scientia ◽

10.1016/s0252-9602(17)30698-7 ◽

1994 ◽

Vol 14 (2) ◽

pp. 130-138 ◽

Cited By ~ 1

Author(s):

Shumo Yu

Keyword(s):

Abelian Group ◽

Harmonic Analysis ◽

Compact Abelian Group ◽

Locally Compact Abelian Group ◽

Locally Compact

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Harmonic Analysis of Spherical Functions on Real Reductive Groups

10.1007/978-3-642-72956-0 ◽

1988 ◽

Cited By ~ 52

Author(s):

Ramesh Gangolli ◽

Veeravalli S. Varadarajan

Keyword(s):

Harmonic Analysis ◽

Spherical Functions ◽

Reductive Groups

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The Research of the Repolarization Process in Solid Solutions (Rb1 – xKx)2ZnCl4 by the Harmonic Analysis Method

Bulletin of the Russian Academy of Sciences Physics ◽

10.3103/s1062873819120074 ◽

2019 ◽

Vol 83 (12) ◽

pp. 1533-1538

Author(s):

V. V. Gorbatenko ◽

B. N. Prasolov ◽

S. A. Gorbatenko ◽

N. V. Datsenko

Keyword(s):

Harmonic Analysis ◽

Solid Solutions ◽

Analysis Method ◽

Harmonic Analysis Method

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Geometric Cardinal Invariants, Maximal Functions and a Measure Theoretic Pigeonhole Principle

Bulletin of Symbolic Logic ◽

10.2178/bsl/1130335207 ◽

2005 ◽

Vol 11 (4) ◽

pp. 517-525

Author(s):

Juris Steprāns

Keyword(s):

Harmonic Analysis ◽

Set Theory ◽

Harmonic Functions ◽

Maximal Functions ◽

Pigeonhole Principle ◽

Cardinal Invariants ◽

Geometric Objects

AbstractIt is shown to be consistent with set theory that every set of reals of size ℵ1 is null yet there are ℵ1 planes in Euclidean 3-space whose union is not null. Similar results will be obtained for other geometric objects. The proof relies on results from harmonic analysis about the boundedness of certain harmonic functions and a measure theoretic pigeonhole principle.

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