Generalized Lebesgue Points for Hajłasz Functions

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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2018-01-01

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Department of Mathematics and Systems Analysis

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en

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12

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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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DOI

10.1155/2018/5637042

Citation

Heikkinen, T 2018, ' Generalized Lebesgue Points for Hajłasz Functions ', Journal of Function Spaces, vol. 2018, 5637042 . https://doi.org/10.1155/2018/5637042

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https://urn.fi/URN:NBN:fi:aalto-201902251808

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[article-cris] Perustieteiden korkeakoulu / SCI