Weighted inequalities related to a Muckenhoupt and Wheeden problem for\n one-side singular integrals

2013/09/25 by María Silvina Riveros, Riveros, María Silvina, Raúl E. Vidal +1 · 1 citation
Mathematics · #42B20 #42B25 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1309.6601

openalex publication_date 2013/09/25 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

In this paper we obtain for T⁺, a one-sided singular integral given by a\nCalder 'on-Zygmund kernel with support in (-\∞,0), a L^p(w) bound when\nw\∈ A₁⁺. A. K. Lerner, S. Ombrosi, and C. P 'erez proved in [ "A₁\nBounds for Calder 'on-Zygmund operators related to a problem of Muckenhoupt and\nWheeden", Math. Res. Lett. \16 (2009), no. 1, 149-156] that this bound\nis sharp with respect to ||w||_A1 and p . We also give a\nL^1,\∞(w) estimate, for a related problem of Muckenhoupt and Wheeden\nfor w\∈ A₁⁺ . We improve the classical results, for one-sided singular\nintegrals, by putting in the inequalities a wider class of weights.\n

Cited by

• An A₂ Theorem for One-Sided Calderón-Zygmund Operators

Related

• Sharp weighted bounds involving A_∞
• Weighted Weak (1,1) estimates for one-sided oscillatory singular integrals
• Sharp weighted bounds for one-sided and multiple integral operators
• L^p bounds for singular integrals and maximal singular integrals with\n rough kernels
• A new sufficient two-weighted bump assumption for L^p boundedness of Calderón-Zygmund operators