Periodization, transference of Muckenhoupt weights, and automatic tight norm estimates for the periodic Hilbert transform

DOI10.1007/s12220-020-00405-2zbMath1471.42014OpenAlexW3023072986MaRDI QIDQ2050697

Earl Berkson

Publication date: 31 August 2021

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12220-020-00405-2

zbMATH Keywords

transferencesharp weighted estimatesperiodic Hilbert transform

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) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Multipliers in one variable harmonic analysis (42A45) Conjugate functions, conjugate series, singular integrals (42A50)

Related Items (2)

Note on a special class of \(A_1 (\mathbb{R})\) weights that exemplify Rubio de Francia's Littlewood-Paley type inequality in the setting of \(A_1 (\mathbb{R})\)-weighted \(L^2\) ⋮ Maximal operators on the infinite-dimensional torus

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Sharp weighted bounds involving \(A_\infty\)
• The sharp weighted bound for general Calderón-Zygmund operators
• Extrapolation and sharp norm estimates for classical operators on weighted Lebesgue spaces
• Extrapolation of weights revisited: new proofs and sharp bounds
• Factorization of \(A_p\) weights
• Multipliers for weighted \(L^p\)-spaces, transference, and the \(q\)-variation of functions
• Analyse harmonique non-commutative sur certains espaces homogènes. Etude de certaines intégrales singulières. (Non-commutative harmonic analysis on certain homogeneous spaces. Study of certain singular integrals.)
• The Ap-Ainfty inequality for general Calderon-Zygmund operators
• On restrictions of multipliers in weighted settings
• Restriction and extension of Fourier multipliers between weighted 𝐿^{𝑝} spaces on ℝⁿ and 𝕋ⁿ
• Constructive Decomposition of BMO Functions and Factorization of A p Weights
• Maximal operators defined by Fourier multipliers
• Operators associated with representations of amenable groups singular integrals induced by ergodic flows, the rotation method and multipliers
• Estimates for Operator Norms on Weighted Spaces and Reverse Jensen Inequalities
• An A_p --A_infty inequality for the Hilbert Transform
• The sharp bound for the Hilbert transform on weighted Lebesgue spaces in terms of the classical A p characteristic
• ERGODIC THEORY AND TRANSLATION-INVARIANT OPERATORS
• On the convergence of multiple Fourier series
• Weighted Norm Inequalities for the Conjugate Function and Hilbert Transform

This page was built for publication: Periodization, transference of Muckenhoupt weights, and automatic tight norm estimates for the periodic Hilbert transform