4 papers
Embeddings of variable Sobolev, Besov, and Triebel-Lizorkin spaces on metric measure spaces
Ryan Alvarado, MichaÅ Dymek, PrzemysÅaw Górka +1
Sobolev-type embeddings on metric measure spaces encode a subtle interaction between the analytic regularity of functions and the geometry of the underlying domain space. In this p…
Logarithmic double phase embeddings with variable exponents: Necessary and Sufficient Conditions
Ankur Pandey, Nijjwal Karak
In this paper, we study the necessary and sufficient conditions in the domain for Sobolev-type embedding of the space where $Φ(x,t):=t^{p(x)}+ a(x) t^{…
Musielak-Orlicz-Sobolev embeddings: Necessary and Sufficient Conditions
Ankur Pandey, Nijjwal Karak
In this paper we study the necessary and sufficient conditions on domain for Musielak-Orlicz-Sobolev embedding of the space where $Φ(x,t):=t^{p(x)}{(\l…
Capacity and Hausdorff measure in Musielak-Orlicz-Sobolev spaces
Ankur Pandey, Nijjwal Karak, Debarati Mondal
In this paper, we show that sets with zero Sobolev -capacity have generalized Hausdorff -measure zero, for some gauge function We also prove that se…