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math.CA2024
Fractional Hardy inequalities and capacity density
Lizaveta Ihnatsyeva, Kaushik Mohanta, Antti V. Vähäkangas
We prove that a pointwise fractional Hardy inequality implies a fractional Hardy inequality, defined via a Gagliardo-type seminorm. The proof consists of two main parts. The first…
math.CA2024
Classifying Triebel-Lizorkin capacities in metric spaces
Juha Lehrbäck, Kaushik Mohanta, Antti V. Vähäkangas
We study non-local or fractional capacities in metric measure spaces. Our main goal is to clarify the relations between relative Hajlasz-Triebel-Lizorkin capacities, potentional Tr…
math.CA2024
Traces of vanishing Hölder spaces
Kaushik Mohanta, Carlos Mudarra, Tuomas Oikari
For an arbitrary subset we introduce and study the three vanishing subspaces of the Hölder space consisting of those functions for which…