Results 61 to 70 of about 2,173 (142)
Bessel potential spaces with variable exponent
, 2007 We show that a variable exponent Bessel potential space coincides with the variable exponent Sobolev space if the Hardy-Littlewood maximal operator is bounded on the underlying variable exponent Lebesgue space.
P. Gurka +2 more
semanticscholar +1 more source
Journal of Inequalities and Applications, 2013 Our aim in this paper is to give Sobolev’s inequality for Riesz potentials of functions in generalized Morrey spaces with variable exponent attaining the value 1 over non-doubling measure spaces.
Y. Sawano, T. Shimomura
semanticscholar +1 more source
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 37, Page 1973-1996, 2004., 2004 Simplified regularization using finite‐dimensional approximations in the setting of Hilbert scales has been considered for obtaining stable approximate solutions to ill‐posed operator equations. The derived error estimates using an a priori and a posteriori choice of parameters in relation to the noise level are shown to be of optimal order with ...
Santhosh George, M. Thamban Nair
wiley +1 more source
An improvement to the John-Nirenberg inequality for functions in critical Sobolev spaces
Advances in Nonlinear Analysis, 2020 It is known that functions in a Sobolev space with critical exponent embed into the space of functions of bounded mean oscillation, and therefore satisfy the John-Nirenberg inequality and a corresponding exponential integrability estimate.
Martínez Ángel D., Spector Daniel
doaj +1 more source
Approximation theory for weighted Sobolev spaces on curves [PDF]
, 2001 17 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.MR#: MR1882649 (2003c:42002)In this paper we present a definition of weighted Sobolev spaces on curves and find general conditions under which the spaces are complete.
Pestana, Domingo +3 more
core +2 more sources
, 2013 In unbounded subset $\Omega$ in $R^n$ we study the operator $u\rightarrow gu$ as an operator defined in the Sobolev space $W^{r,p}(\Omega)$ and which takes values in $L^p(\Omega)$.
Canale, Anna
core +1 more source
Another extension of Orlicz‐Sobolev spaces to metric spaces
Abstract and Applied Analysis, Volume 2004, Issue 1, Page 1-26, 2004., 2004 We propose another extension of Orlicz‐Sobolev spaces to metric spaces based on the concepts of the Φ‐modulus and Φ‐capacity. The resulting space NΦ1 is a Banach space. The relationship between NΦ1 and MΦ1 (the first extension defined in Aïssaoui (2002)) is studied.
Noureddine Aïssaoui
wiley +1 more source
The concentration-compactness principles for Ws,p(·,·)(ℝN) and application
Advances in Nonlinear Analysis, 2020 We obtain a critical imbedding and then, concentration-compactness principles for fractional Sobolev spaces with variable exponents. As an application of these results, we obtain the existence of many solutions for a class of critical nonlocal problems ...
Ho Ky, Kim Yun-Ho
doaj +1 more source
On functional reproducing kernels
Open Mathematics, 2023 We show that even if a Hilbert space does not admit a reproducing kernel, there could still be a kernel function that realizes the Riesz representation map.
Zhou Weiqi
doaj +1 more source
Embeddings of α-Modulation Spaces [PDF]
, 2012 2010 Mathematics Subject Classification: 42B35, 46E35.We show upper and lower embeddings of α1-modulation spaces in α2-modulation spaces for 0 ≤ α1 ≤ α2 ≤ 1, and prove partial results on the sharpness of the ...
Toft, Joachim, Wahlberg, Patrik
core