5 citations · 6 across the 12 of their papers we have counts for
15 papers
Embeddings of variable Sobolev, Besov, and Triebel-Lizorkin spaces on metric measure spaces
Ryan Alvarado, Michał Dymek, Przemysław 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^{q(x…
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…
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)}{(\log(…
Capacity in Besov and Triebel-Lizorkin spaces with generalized smoothness
Nijjwal Karak, Debarati Mondal
We prove a lower bound estimate for capacities in Hajlasz-Besov, Hajlasz-Triebel-Lizorkin and Hajlasz-Sobolev spaces with generalized smoothness defined on metric spaces in terms o…
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,…
Removable sets for weighted Orlicz-Sobolev spaces
Nijjwal Karak
The aim in the present paper is to study removable sets for weighted Orlicz-Sobolev spaces. We generalize the definition of porous sets and show that the porous sets lying in a hyp…
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…
Capacities and Hausdorff measures on metric spaces
Nijjwal Karak, Pekka Koskela
In this article, we show that in a -doubling space that supports a -Poincaré inequality and satisfies a chain condition, sets of -capacity zero have gene…
Lebesgue points via the Poincaré inequality
Nijjwal Karak, Pekka Koskela
In this article, we show that in a -doubling space which satisfies a chain condition, if we have a -Poincaré inequality for a pair of functions wher…
Removable sets for Orlicz-Sobolev spaces
Nijjwal Karak
We study removable sets for the Orlicz-Sobolev space for functions of the form We show that -porous sets lying in a hyperplane are removabl…