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Marcinkiewicz Summability Of Fourier Series, Lebesgue Points And Strong Summability

F. Weisz
Published 2017 · Mathematics

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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 holds for a weaker version of Lebesgue points, for the so called modified Lebesgue points of $${f \in L_p(\mathbb{T}^d)}$$f∈Lp(Td), whenever $${1 < p < \infty}$$1
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