\(\ell^p(\mathbb{Z}^d)\)-improving properties and sparse bounds for discrete spherical maximal averages

DOI10.1007/s11854-021-0150-yzbMath1470.42030arXiv1805.09925OpenAlexW3163555283MaRDI QIDQ2046129

Robert Kesler

Publication date: 17 August 2021

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.09925

zbMATH Keywords

reverse Hölder classesMuckenhoupt classesweighted inequalities for sparse operators

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Irregularities of distribution, discrepancy (11K38)

Related Items (3)

Improving estimates for discrete polynomial averages ⋮ Lattice points problem, equidistribution and ergodic theorems for certain arithmetic spheres ⋮ Quantitative \(l^p\)-improving for discrete spherical averages along the primes

Cites Work

• A pointwise estimate for positive dyadic shifts and some applications
• Sparse bounds for oscillatory and random singular integrals
• An elementary proof of the \(A_{2}\) bound
• Averages in the plane over convex curves and maximal operators
• Discrete fractional Radon transforms and quadratic forms
• On the distribution of lattice points on spheres and level surfaces of polynomials
• Sparse bounds for the discrete cubic Hilbert transform
• Sparse endpoint estimates for Bochner-Riesz multipliers on the plane
• Two discrete fractional integral operators revisited
• Uniform sparse bounds for discrete quadratic phase Hilbert transforms
• A note on twisted discrete singular Radon transforms
• Sparse bounds for spherical maximal functions
• \(\ell^p\)-improving inequalities for discrete spherical averages
• \(\ell ^p\left(\mathbb {Z}^d\right)\)-estimates for discrete operators of Radon type: variational estimates
• $L^p$ boundedness of discrete singular Radon transforms
• A Remark on Singular Calderon-Zygmund Theory
• Maximal functions: Spherical means
• Problems in harmonic analysis related to curvature
• A Discrete Quadratic Carleson Theorem on withℓ²a Restricted Supremum
• Sparse Bounds for Random Discrete Carleson Theorems
• A generalization of Bourgain’s circular maximal theorem

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