Marcinkiewicz summability of Fourier series, Lebesgue points and strong summability
Sign Up to like & getrecommendations! Published in 2017 at "Acta Mathematica Hungarica"
DOI: 10.1007/s10474-017-0737-z
Abstract: Under some conditions on $${\theta}$$θ, we characterize the set of convergence of the Marcinkiewicz-$${\theta\mbox{-}}$$θ-means of a function $${f \in L_1(\mathbb{T}^d)}$$f∈L1(Td). More exactly, the $${\theta\mbox{-}}$$θ-means converge to f at each modified strong Lebesgue point. The same… read more here.
Keywords: summability; lebesgue points; lebesgue; marcinkiewicz ... See more keywords
Lp Estimates of certain rough parametric Marcinkiewicz functions
Sign Up to like & getrecommendations! Published in 2019 at "Frontiers of Mathematics in China"
DOI: 10.1007/s11464-019-0792-6
Abstract: We prove Lp estimates of a class of parametric Marcinkiewicz integral operators when their kernels satisfy only the \(L^1(\mathbb{S}^{n-1})\) integrability condition. The obtained Lp estimates resolve a problem left open in previous work. Our argument… read more here.
Keywords: parametric marcinkiewicz; rough parametric; certain rough; estimates certain ... See more keywords