Calderón-Zygmund operators on generalized Lebesgue spaces $L^{p(\cdot)}$ and problems related to fluid dynamics

By Lars Diening, M. Růžička. 2003

361 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/11e7f80db3d5e7a95cb35ef9e901cae09c9efebc

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Maximal function on Musielak–Orlicz spaces and generalized Lebesgue spaces (2005, background): “8 we can state the results of [8] under weaker assumptions.”
A capacity approach to the Poincare inequality and Sobolev imbeddings in variable exponent Sobolev spaces (2004, neutral): “[4–7, 9–11, 17, 22].”
TRIGONOMETRIC APPROXIMATION IN GENERALIZED LEBESGUE SPACES L p(x) (2010, background): “We refer to [13], [9], [10] and [7] for properties above and for more general information about Lp(x) spaces.”
Boundedness of Maximal and Singular Operators in Morrey Spaces with Variable Exponent (2008, methodology): “For mapping properties of maximal functions and singular integrals on Lebesgue spaces with variable exponent we refer to [9], [10], [7], [6], [19]-[20], [26], [13] (see also [29], [17] and references therein).”
Sobolev embeddings in metric measure spaces with variable dimension (2006, background): “[1,3,6,17,24,25], and some studies in the metric space setting have also appeared [12,18–20,27].”
Gradient estimates for the p (x)-Laplacean system (2005, methodology): “This slightly reinforces the condition considered by Diening and Růžička [12], where the right hand side of (6) is supposed to be a finite number rather than zero, see (18), and plays a central role in the regularity analysis of solutions of this kind of problems; it is essentially optimal in order ”
An atomic decomposition of variable Besov and Triebel-Lizorkin spaces (2009, background): “Moreover, these spaces have been applied to partial differential equations and the calculus of variation, see [1, 3, 4, 5, 6, 7, 8, 10, 11, 12, 16, 17, 18, 19, 21, 22, 29] and references therein.”
Monotone operator theory for unsteady problems in variable exponent spaces (2012, background): “The following extension result can be found in 13 , 14 , 27 .”