Zobrazeno 1 - 10
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pro vyhledávání: '"Karak, Nijjwal"'
Autor:
Pandey, Ankur, Karak, Nijjwal
In this paper we study the necessary and sufficient conditions on domain for Musielak-Orlicz-Sobolev embedding of the space $W^{1,\Phi(\cdot,\cdot)}(\Omega)$ where $\Phi(x,t):=t^{p(x)}{(\log(e+t))}^{q(x)}.$
Comment: 15 pages
Comment: 15 pages
Externí odkaz:
http://arxiv.org/abs/2406.08091
Autor:
Karak, Nijjwal, Mondal, Debarati
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 of Netrusov-Hausdorff content or Hausdorff content.
Comment: To ap
Comment: To ap
Externí odkaz:
http://arxiv.org/abs/2401.12020
Autor:
Karak, Nijjwal
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 generalized Hausdorff $h$-measure zero for a suitable gauge function $h.$<
Externí odkaz:
http://arxiv.org/abs/1910.03920
Autor:
Karak, Nijjwal
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 \cite{Cia96} (and \cite{Cia06}).
Comment: 10 pages, Funding agenc
Comment: 10 pages, Funding agenc
Externí odkaz:
http://arxiv.org/abs/1903.02808
Autor:
Karak, Nijjwal
We prove that if the Sobolev embedding $M^{1,p}(X)\hookrightarrow L^q(X)$ holds for some $q>p\geq 1$ in a metric measure space $(X,d,\mu),$ then a constant $C$ exists such that $\mu(B(x,r))\geq Cr^n$ for all $x\in X$ and all $0
Externí odkaz:
http://arxiv.org/abs/1903.02342
Autor:
Karak, Nijjwal
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 metric measure space and lower bound for measure of balls either in the
Externí odkaz:
http://arxiv.org/abs/1803.08499
Autor:
Karak, Nijjwal
In this paper, we investigate the relation between Sobolev-type embeddings of Haj{\l}asz-Besov spaces (and also Haj{\l}asz-Triebel-Lizorkin spaces) defined on a metric measure space $(X,d,\mu)$ and lower bound for the measure $\mu.$ We prove that if
Externí odkaz:
http://arxiv.org/abs/1803.00224
Publikováno v:
Revista Matematica Complutense; Sep2024, Vol. 37 Issue 3, p695-711, 17p
Autor:
Heikkinen, Toni, Karak, Nijjwal
Publikováno v:
In Journal of Functional Analysis 15 January 2022 282(2)