Generalized Lebesgue Points for Hajłasz Functions

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Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2018-01-01
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Language
en
Pages
12
Series
Journal of Function Spaces, Volume 2018
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.
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Heikkinen , T 2018 , ' Generalized Lebesgue Points for Hajłasz Functions ' , Journal of Function Spaces , vol. 2018 , 5637042 . https://doi.org/10.1155/2018/5637042