Oscillation inequalities for Carleson--Dunkl operator

2024/06/16 by Słomian, Wojciech
#42A38 (Primary) #42B10 #42B25 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.10896

Abstract

In this paper, we establish estimates for the oscillation seminorm for the so-called Carleson--Dunkl operator on weighted L^p(ℝ,w(x)|x|^2α+1\rm dx) spaces with power weights w(x)=|x|^β. As a result, we obtain oscillation estimates for the standard Carleson operator on L_{\rm rad}^p(ℝⁿ,|x|^β\rm dx). As a byproduct, we obtain a transference principle for radial multipliers on L_{\rm rad}^p spaces, in the spirit of the Rubio de Francia transference principle.

Related

• On weighted norm inequalities for the Carleson operator
• L^p estimates for an oscillating Dunkl multiplier
• Oscillatory integrals related to Carleson's theorem: fractional monomials
• Classes of operators on weighted function spaces in Dunkl analysis
• A type of oscillatory integral operator and its applications