1 citations · 1 across the 2 of their papers we have counts for
6 papers
Triebel-Lizorkin capacity and Hausdorff measure in metric spaces
Nijjwal Karak
We provide a upper bound for Triebel-Lizorkin capacity in metric settings in terms of Hausdorff measure. On the other hand, we also prove that the sets with zero capacity have gene…
A necessary condition on domains for optimal Orlicz-Sobolev embeddings
Nijjwal Karak
We provide a necessary condition on the regularity of domains for the optimal embeddings of first order (and higher order) Orlicz-Sobolev spaces into Orlicz spaces in the sense of…
Sobolev embedding implies regularity of measure in metric measure spaces
Nijjwal Karak
We prove that if the Sobolev embedding holds for some in a metric measure space then a constant exists such that $μ(B(…
Lower bound of measure and embeddings of Sobolev, Besov and Triebel-Lizorkin spaces
Nijjwal Karak
In this article, we study the relation between Sobolev-type embeddings for Sobolev spaces or Besov spaces or Triebel-Lizorkin spaces defined either on a doubling or on a geodesic m…
Measure density and Embeddings of Hajłasz-Besov and Hajłasz-Triebel-Lizorkin spaces
Nijjwal Karak
In this paper, we investigate the relation between Sobolev-type embeddings of Hajłasz-Besov spaces (and also Hajłasz-Triebel-Lizorkin spaces) defined on a metric measure space $(X,…
Generalized Lebesgue points for Sobolev functions
Nijjwal Karak
In this article, we show that a function where is a doubling metric measure space, has generalized Lebesgue points outside a set of $\m…