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Reduction of integration domain in Triebel–Lizorkin spaces

Volume 259 / 2021

Artur Rutkowski Studia Mathematica 259 (2021), 121-152 MSC: Primary 46E35; Secondary 31C25. DOI: 10.4064/sm190729-14-5 Published online: 21 December 2020


We investigate the comparability of generalized Triebel–Lizorkin and Sobolev seminorms on uniform and nonuniform domains when the integration domain is truncated according to the distance from the boundary. We provide numerous examples of kernels and domains in which the comparability does and does not hold.


  • Artur RutkowskiFaculty of Pure and Applied Mathematics
    Wrocław University of Science and Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland

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