Generalized Lebesgue Points for Hajłasz Functions

Toni Heikkinen*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
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Abstract

Let X be a quasi-Banach function space over a doubling metric measure space P. Denote by αX the generalized upper Boyd index of X. We show that if αX<∞ and X has absolutely continuous quasinorm, then quasievery point is a generalized Lebesgue point of a quasicontinuous Hajłasz function uṀs,X. Moreover, if αX<(Q+s)/Q, then quasievery point is a Lebesgue point of u. As an application we obtain Lebesgue type theorems for Lorentz-Hajłasz, Orlicz-Hajłasz, and variable exponent Hajłasz functions.

Original languageEnglish
Article number5637042
Number of pages12
JournalJournal of Function Spaces
Volume2018
DOIs
Publication statusPublished - 1 Jan 2018
MoE publication typeA1 Journal article-refereed

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