Nijjwal Karak

activity

20152026

most citedSobolev embedding implies regularity of measure in metric measure spaces

1 citations · 1 across the 7 of their papers we have counts for

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Showing 2019Show all

3 papers · 1 filter

math.FA2019

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…

math.FA2019

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…

math.FA2019★ 1 cited

Sobolev embedding implies regularity of measure in metric measure spaces

Nijjwal Karak

We prove that if the Sobolev embedding $M^{1, p} (X) ↪ L^{q} (X)$ holds for some $q > p \geq 1$ in a metric measure space $(X, d, μ),$ then a constant $C$ exists such that $μ(B(…