The Boundedness of Alternative General Gaussian Singular Integrals with respect to the Gaussian measure
Eduard Nava, Ebner Pineda, Wilfredo Urbina
TL;DR
This paper introduces a new class of Gaussian singular integrals called general alternative Gaussian singular integrals and investigates their boundedness in Lp spaces and weak (1,1) boundedness with respect to the Gaussian measure.
Contribution
It defines a novel class of Gaussian singular integrals and establishes their boundedness properties, extending previous work by Pérez, Aimar, Forzani, and Scotto.
Findings
Proves boundedness of the new integrals in Lp for p > 1.
Establishes weak (1,1) boundedness of the integrals.
Extends classical results to a broader class of Gaussian singular integrals.
Abstract
In this paper we introduce a new class of Gaussian singular integrals, the general alternative Gaussian singular integrals and study the boundedness of them in Lp, p >1 and its weak (1,1) boundedness with respect to the Gaussian measure following the works of S. P\'erez and H. Aimar, L. Forzani and R. Scotto respectively.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Mathematical functions and polynomials · Geometric Analysis and Curvature Flows