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Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2017, Volume 453, Issue 1, pp. 434 - 457
In this paper, we obtain the Franke–Jawerth embedding property of Hajłasz–Besov and Hajłasz–Triebel–Lizorkin spaces on a measure metric space... 
Pointwise multiplier | Triebel–Lizorkin space | Embedding | Hajłasz gradient | Hyperbolic filling | Besov space | MATHEMATICS | MATHEMATICS, APPLIED | Hajlasz gradient | Triebel-Lizorkin space | HAJLASZ-SOBOLEV SPACES | Algebra
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 09/2017, Volume 160, pp. 135 - 158
.... Applications to boundedness of the Littlewood–Paley operators on Lipschitz spaces and Hajłasz–Sobolev spaces are considered. 
Lipschitz space | Littlewood–Paley operator | Hajłasz–Sobolev space | BMO space | Poincaré inequality | MATHEMATICS | MATHEMATICS, APPLIED | METRIC-SPACES | Hajlasz-Sobolev space | BMO | HARDY-SPACES | Poincare inequality | Littlewood-Paley operator | HAJLASZ-SOBOLEV SPACES
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... 
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
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2009, Volume 353, Issue 2, pp. 489 - 496
Journal Article
Mathematical Research Letters, ISSN 1073-2780, 2008, Volume 15, Issue 4, pp. 727 - 744
We establish pointwise characterizations of functions in the Hardy-Sobolev spaces H-1,H-p within the range p is an element of (n/(n + 1), 1... 
Pointwise inequalities | Hajłasz-Sobolev spaces | Hardy inequalities | Hardy-Sobolev spaces | MATHEMATICS | INEQUALITIES | R(N) | BOUNDARY-VALUE-PROBLEMS | SMOOTH DOMAIN | SUBSETS | HP SPACES
Journal Article
Siberian Mathematical Journal, ISSN 0037-4466, 9/2015, Volume 56, Issue 5, pp. 822 - 826
We consider the generalized Hajłasz–Sobolev classes W α p (X), α > 0, on ultrametric measure spaces X with doubling condition... 
Luzin approximation | Lebesgue point | Hajłasz-Sobolev class | Mathematics, general | Mathematics | convergence rate for Steklov averages | capacity
Journal Article
by Badr, N and Dafni, G
Journal of Functional Analysis, ISSN 0022-1236, 2010, Volume 259, Issue 6, pp. 1380 - 1420
Several possible notions of Hardy–Sobolev spaces on a Riemannian manifold with a doubling measure are considered... 
Hardy–Sobolev spaces | Hajłasz–Sobolev spaces | Metric measure spaces | Atomic decomposition
Journal Article
Potential Analysis, ISSN 0926-2601, 2/2017, Volume 46, Issue 2, pp. 227 - 259
Journal Article
Frontiers of Mathematics in China, ISSN 1673-3452, 9/2006, Volume 1, Issue 3, pp. 480 - 483
Journal Article
Publicacions matemàtiques, ISSN 0214-1493, 1/2014, Volume 58, Issue 2, pp. 379 - 399
Motivated by the results of Korry, and Kinnunen and Saksman, we study the behaviour of the discrete fractional maximal operator on fractional Hajłasz spaces, Hajłasz-Besov, and Hajłasz-Triebel... 
Metric measure space | Fractional maximal function | Besov space | Fractional Sobolev space | Triebel-Lizorkin space | Fractional sobolev space | MATHEMATICS | REGULARITY | metric measure space | Triebel Lizorkin space | HAJLASZ-SOBOLEV SPACES | fractional Sobolev space | fractional maximal function | 42B25 | 46E35
Journal Article
Journal of functional analysis, ISSN 0022-1236, 2019, Volume 276, Issue 6, pp. 1853 - 1874
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 11/2017, Volume 369, Issue 11, pp. 7631 - 7655
In this article, the authors characterize Besov spaces \dot B^{\alpha }_{p,q}(\mathbb{R}^n) and Triebel-Lizorkin spaces... 
Pointwise characterization | Ball average | Besov space | Calderón reproducing formula | Triebel-Lizorkin space | pointwise characterization | MATHEMATICS | METRIC-SPACES | Calderon reproducing formula | ball average | EXTENSION | HAJLASZ-SOBOLEV SPACES
Journal Article
Czechoslovak Mathematical Journal, ISSN 0011-4642, 6/2016, Volume 66, Issue 2, pp. 371 - 394
Journal Article
Potential Analysis, ISSN 0926-2601, 8/2016, Volume 45, Issue 2, pp. 201 - 227
In this paper we introduce Bessel potentials and the Sobolev potential spaces resulting from them in the context of Ahlfors regular metric spaces... 
Geometry | Potential Theory | Functional Analysis | Bessel potential | Probability Theory and Stochastic Processes | Mathematics | 43A85 | Sobolev spaces | Besov spaces | Ahlfors spaces | Fractional derivative | MATHEMATICS | BESOV | HAJLASZ-SOBOLEV SPACES | Mathematics - Classical Analysis and ODEs
Journal Article
Forum Mathematicum, ISSN 0933-7741, 03/2009, Volume 21, Issue 2, pp. 259 - 298
An RD-space X is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in X, or equivalently, that there exists a constant a(0... 
BROWNIAN-MOTION | MATHEMATICS | FRACTALS | MATHEMATICS, APPLIED | LIE-GROUPS | POLYNOMIAL-GROWTH | METRIC MEASURE-SPACES | HARDY-SPACES | QUASI-CONFORMAL MAPPINGS | HAJLASZ-SOBOLEV SPACES | HOMOGENEOUS TYPE | SINGULAR-INTEGRALS
Journal Article
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