Lebesgue points of Besov and Triebel–Lizorkin spaces with generalized smoothness

Z Li, D Yang, W Yuan - Mathematics, 2021 - mdpi.com
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 …

Capacity in Besov and Triebel–Lizorkin spaces with generalized smoothness

N Karak, D Mondal - Georgian Mathematical Journal, 2024 - degruyter.com
We prove a lower bound estimate for capacities in Hajłasz–Besov, Hajłasz–Triebel–Lizorkin
and Hajłasz–Sobolev spaces with generalized smoothness defined on metric spaces in …

Besov and Triebel-Lizorkin capacity in metric spaces

N Karak, D Mondal - Mathematica Slovaca, 2023 - degruyter.com
We prove a lower bound estimate for Hajłasz-Besov capacity in metric spaces in terms of
Netrusov-Hausdorff content. We also prove a similar estimate for Hajłasz-Triebel-Lizorkin …

Differentiability of logarithmic Besov functions in terms of capacities

S Wu, D Yang, W Yuan - Banach Journal of Mathematical Analysis, 2022 - Springer
In this article, the authors investigate the differentiability of functions from logarithmic Besov
spaces via establishing the high order analogue of the Lebesgue differentiation theorem for …