Photo from wikipedia
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… Click to show full 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 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
Keywords:
summability;
lebesgue points;
lebesgue;
marcinkiewicz;
theta mbox;
strong summability
Journal Title: Acta Mathematica Hungarica
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!
Journal Title: Acta Mathematica Hungarica
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!