Lebesgue Points for Orlicz-Sobolev Functions on Metric Measure Spaces

2011 ◽  
Vol 57 (Supliment) ◽  
Author(s):  
Marcelina Mocanu
Keyword(s):  
Metric Measure Spaces ◽  
Lebesgue Points ◽  
Sobolev Functions ◽  
Measure Spaces

Sobolev Extensions of Hölder Continuous and Characteristic Functions on Metric Spaces

2007 ◽  
Vol 59 (6) ◽  
pp. 1135-1153 ◽  
Author(s):  
Anders Björn ◽  
Jana Björn ◽  
Nageswari Shanmugalingam
Keyword(s):  
Metric Spaces ◽  
Continuous Functions ◽  
Characteristic Functions ◽  
Metric Measure Spaces ◽  
Hölder Continuous ◽  
Geometric Conditions ◽  
Sobolev Functions ◽  
Measure Spaces ◽  
Hölder Continuous Functions

AbstractWe study when characteristic and Hölder continuous functions are traces of Sobolev functions on doubling metric measure spaces. We provide analytic and geometric conditions sufficient for extending characteristic and Hölder continuous functions into globally defined Sobolev functions.

scholarly journals Lebesgue Points of Besov and Triebel–Lizorkin Spaces with Generalized Smoothness

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2724
Author(s):  
Ziwei Li ◽  
Dachun Yang ◽  
Wen Yuan
Keyword(s):  
Lebesgue Point ◽  
Metric Measure Spaces ◽  
Exceptional Sets ◽  
Lebesgue Points ◽  
Measure Spaces ◽  
Zero Capacity

In this article, the authors study the Lebesgue point of functions from Hajłasz–Sobolev, Besov, and Triebel–Lizorkin spaces with generalized smoothness on doubling metric measure spaces and prove that the exceptional sets of their Lebesgue points have zero capacity via the capacities related to these spaces. In case these functions are not locally integrable, the authors also consider their generalized Lebesgue points defined via the γ-medians instead of the classical ball integral averages and establish the corresponding zero-capacity property of the exceptional sets.

scholarly journals Lower estimates of heat kernels for non-local Dirichlet forms on metric measure spaces

2017 ◽  
Vol 272 (8) ◽  
pp. 3311-3346 ◽  
Author(s):  
Alexander Grigor'yan ◽  
Eryan Hu ◽  
Jiaxin Hu
Keyword(s):  
Dirichlet Forms ◽  
Heat Kernels ◽  
Metric Measure Spaces ◽  
Measure Spaces ◽  
Non Local

scholarly journals A note on the extension of BV functions in metric measure spaces

2008 ◽  
Vol 340 (1) ◽  
pp. 197-208 ◽  
Author(s):  
Annalisa Baldi ◽  
Francescopaolo Montefalcone
Keyword(s):  
Metric Measure Spaces ◽  
Bv Functions ◽  
Measure Spaces
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