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Czechoslovak Mathematical Journal, ISSN 0011-4642, 3/2017, Volume 67, Issue 1, pp. 143 - 150
...Czechoslovak Mathematical Journal, 67 (142) (2017), 143{150 GENERALIZED LEBESGUE POINTS FOR SOBOLEV FUNCTIONS Nijjwal Karak, Jyväskylä Received July 27, 2015... 
Ordinary Differential Equations | 46E35 | median | generalized Lebesgue point | Sobolev space | Analysis | Convex and Discrete Geometry | metric measure space | 28A78 | Mathematics, general | Mathematics | Mathematical Modeling and Industrial Mathematics | MATHEMATICS | CAPACITIES | HAUSDORFF MEASURES | INEQUALITY | METRIC MEASURE-SPACES | OSCILLATION
Journal Article
中国科学:数学英文版, ISSN 1674-7283, 2015, Volume 58, Issue 8, pp. 1697 - 1706
... Berlin Heidelberg 2015 math.scichina.com link.springer.com Lebesgue points via the Poincar´ e inequality KARAK Nijjwal ∗ & KOSKELA Pekka Department of Mathematics... 
格点 | 庞加莱 | 空间 | poincare不等式 | 链条件 | 双功能 | Q -doubling space | 46E35 | Lebesgue point | 28A15 | 28A78 | Mathematics | Applications of Mathematics | Poincaré inequality | Q-doubling space | Equality
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 07/2019, Volume 475, Issue 1, pp. 966 - 984
In this paper, we investigate the relation between Sobolev-type embeddings of Hajłasz-Besov spaces (and also Hajłasz-Triebel-Lizorkin spaces) defined on a... 
Measure density | Hajłasz-Triebel-Lizorkin space | Hajłasz-Besov space | MATHEMATICS | MATHEMATICS, APPLIED | EXTENSIONS | Hajlasz-Besov space | Hajlasz-Triebel-Lizorkin space | SOBOLEV
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 01/2020, Volume 293, Issue 1, pp. 120 - 128
In this article, we study the relation between Sobolev‐type embeddings for Sobolev spaces or Hajłasz–Besov spaces or Hajłasz–Triebel–Lizorkin spaces defined on... 
Hajłasz–Sobolev space | 42B35 | 46E35 | Hajłasz–Besov space | Hajłasz–Triebel–Lizorkin space and measure density | MATHEMATICS | Hajlasz-Besov space | Hajlasz-Triebel-Lizorkin space and measure density | Hajlasz-Sobolev space | MEASURE DENSITY
Journal Article
10/2019
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... 
Mathematics - Functional Analysis
Journal Article
Mathematica Slovaca, ISSN 0139-9918, 06/2020, Volume 70, Issue 3, pp. 617 - 624
...a o DOI: 10.1515/ms-2017-0376 Math. Slovaca 70 (2020), No. 3, 617–624 TRIEBEL-LIZORKIN CAPACITY AND HAUSDORFF MEASURE IN METRIC SPACES Nijjwal Karak... 
31E05 | Hausdorff measure | Triebel-Lizorkin spaces | 31B15 | capacity | MATHEMATICS | LEBESGUE POINTS | EXTENSION | BESOV CAPACITY | Metric space | Upper bounds
Journal Article
03/2019
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... 
Mathematics - Functional Analysis
Journal Article
03/2019
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 $C$... 
Mathematics - Functional Analysis
Journal Article
03/2018
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... 
Mathematics - Functional Analysis
Journal Article
03/2018
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... 
Mathematics - Functional Analysis
Journal Article
Computational Methods and Function Theory, ISSN 1617-9447, 9/2019, Volume 19, Issue 3, pp. 473 - 486
... Nijjwal Karak 1 Received: 7 May 2018 / Revised: 3 December 2018 / Accepted: 29 March 2019 / Published online: 20 July 2019 © Springer-Verlag GmbH Germany, part... 
Removable sets | Weighted orlicz–sobolev spaces | Computational Mathematics and Numerical Analysis | Functions of a Complex Variable | Analysis | Mathematics | Porosity | 31B15 | MATHEMATICS | Weighted orlicz-sobolev spaces | MATHEMATICS, APPLIED | THEOREMS
Journal Article
08/2016
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... 
Mathematics - Functional Analysis
Journal Article
06/2015
In this article, we show that a function $f\in M^{s,p}(X),$ $0 Mathematics - Functional Analysis
Journal Article
Potential Analysis, ISSN 0926-2601, 11/2015, Volume 43, Issue 4, pp. 675 - 694
...Potential Anal (2015) 43:675–694 DOI 10.1007/s11118-015-9491-4 Removable Sets for Orlicz-Sobolev Spaces Nijjwal Karak 1 Received: 31 August 2013 / Accepted: 24... 
Geometry | Removable sets | Potential Theory | Functional Analysis | Orlicz-Sobolev spaces | Probability Theory and Stochastic Processes | Mathematics | Porosity | 31B15 | MATHEMATICS
Journal Article
08/2014
We study removable sets for the Orlicz-Sobolev space $W^{1,\Psi},$ for functions of the form $\Psi(t)=t^p\log^{\lambda}(e+t).$ We show that... 
Mathematics - Functional Analysis
Journal Article
08/2014
In this article, we show that in a $Q$-doubling space $(X,d,\mu),$ $Q>1,$ that supports a $Q$-Poincar\'e inequality and satisfies a chain condition, sets of... 
Mathematics - Functional Analysis
Journal Article
08/2014
In this article, we show that in a $Q$-doubling space $(X,d,\mu),$ $Q>1,$ which satisfies a chain condition, if we have a $Q$-Poincar\'e inequality for a pair... 
Mathematics - Functional Analysis
Journal Article
Revista Matematica Complutense, ISSN 1139-1138, 09/2015, Volume 28, Issue 3, pp. 733 - 740
In this article, we show that in a Q-doubling space , that supports a Q-Poincar, inequality and satisfies a chain condition, sets of Q-capacity zero have... 
Generalized Hausdorff measure | Capacity | Poincaré inequality | MATHEMATICS | MATHEMATICS, APPLIED | SOBOLEV SPACES | Poincare inequality
Journal Article
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