Maximal Functions, Littlewood–Paley Theory, Riesz Transforms and Atomic Decomposition in the Multi-parameter Flag Setting [PDF]
Memoirs of the American Mathematical Society, 2022 In this paper, we develop via real variable methods various characterisations of the Hardy spaces in the multi-parameter flag setting. These characterisations include those via, the non-tangential and radial maximal function, the Littlewood–Paley square function and area integral, Riesz transforms and the atomic decomposition in the multi-parameter ...
Yongsheng Han +3 more
openaire +2 more sources
Littlewood-Paley Characterizations of Hardy-Type Spaces Associated with Ball Quasi-Banach Function Spaces [PDF]
Complex Analysis and Operator Theory, 2019 Let X be a ball quasi-Banach function space on $${{\mathbb {R}}}^n$$ R n . In this article, assuming that the powered Hardy–Littlewood maximal operator satisfies some Fefferman–Stein vector-valued maximal inequality on X and is bounded on the associated ...
D. Chang +3 more
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Harmonic Functions, Conjugate Harmonic Functions and the Hardy Space $$H^1$$H1 in the Rational Dunkl Setting [PDF]
Journal of Fourier Analysis and Applications, 2018 In this work we extend the theory of the classical Hardy space $$H^1$$H1 to the rational Dunkl setting. Specifically, let $$\Delta $$Δ be the Dunkl Laplacian on a Euclidean space $$\mathbb {R}^N$$RN. On the half-space $$\mathbb {R}_+\times \mathbb {R}^N$$
Jean-Philippe Anker +2 more
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A Complete Real-Variable Theory of Hardy Spaces on Spaces of Homogeneous Type [PDF]
Journal of Fourier Analysis and Applications, 2018 Let $$(X,d,\mu )$$(X,d,μ) be a space of homogeneous type, with the upper dimension $$\omega $$ω, in the sense of Coifman and Weiss. Assume that $$\eta $$η is the smoothness index of the wavelets on X constructed by Auscher and Hytönen.
Ziyi He +5 more
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Calderón–Zygmund operators in the Bessel setting [PDF]
Monatshefte für Mathematik (Print), 2010 We study several fundamental operators in harmonic analysis related to Bessel operators, including maximal operators related to heat and Poisson semigroups, Littlewood–Paley–Stein square functions, multipliers of Laplace transform type and Riesz ...
J. Betancor, A. Castro, A. Nowak
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Extrapolation to mixed norm spaces and applications
Acta et commentationes Universitatis Tartuensis de mathematica, 2021 This paper establishes extrapolation theory to mixed norm spaces. By applying this extrapolation theory, we obtain the mapping properties of the Rubio de Francia Littlewood-Paley functions and the geometrical maximal functions on mixed norm spaces.
K. Ho
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A Non-archimedean Variant of Littlewood–Paley Theory for Curves [PDF]
Journal of Geometric Analysis, 2022 We prove a variant of a square function estimate for the extension operator associated to the moment curve in non-archimedean local fields. The arguments rely on a structural analysis of congruences (sublevel sets) of univariate polynomials over field ...
J. Hickman, James Wright
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Subdyadic square functions and applications to weighted harmonic analysis [PDF]
, 2015 Through the study of novel variants of the classical Littlewood–Paley–Stein g -functions, we obtain pointwise estimates for broad classes of highly-singular Fourier multipliers on R d satisfying regularity hypotheses adapted to fine (subdyadic) scales ...
David Beltran, Jonathan Bennett
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Product Hardy, BMO spaces and iterated commutators associated with Bessel Schrodinger operators [PDF]
Indiana University Mathematics Journal, 2017 In this paper we establish the product Hardy spaces associated with the Bessel Schr\"odinger operator introduced by Muckenhoupt and Stein, and provide equivalent characterizations in terms of the Bessel Riesz transforms, non-tangential and radial maximal
J. Betancor +4 more
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Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part III: Harmonic analysis of elliptic operators [PDF]
, 2006 This is the third part of a series of four articles on weighted norm in- equalities, o-diagonal estimates and elliptic operators. For L in some class of elliptic operators, we study weighted norm L p inequalities for singular "non-integral" opera- tors ...
P. Auscher, J. M. Martell
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