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
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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
On Rough Parametric Marcinkiewicz Integrals Along Certain Surfaces
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DOI: 10.3390/math13081287
Abstract: In this paper, we study rough Marcinkiewicz integrals associated with surfaces defined by ΨP,ϕ={(˜P(w),ϕ(w)):w∈Rm}. We establish the Lp-boundedness of these integrals when the kernel functions lie in the Lq(Sm−1) space. Combining this result with Yano’s… read more here.
Keywords: along certain; integrals along; parametric marcinkiewicz; marcinkiewicz integrals ... See more keywords
A Note on Generalized Parabolic Marcinkiewicz Integrals with Grafakos-Stefanov Kernels
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DOI: 10.3390/sym17030429
Abstract: This paper focuses on studying the generalized Marcinkiewicz integral operators with mixed homogeneity over symmetric spaces. By making an appropriate decomposition of the aforementioned operators and tracking certain estimates, the boundedness of these operators is… read more here.
Keywords: marcinkiewicz integrals; parabolic marcinkiewicz; grafakos stefanov; marcinkiewicz ... See more keywords