The Experts below are selected from a list of 156234 Experts worldwide ranked by ideXlab platform
Piotr Hajlasz - One of the best experts on this subject based on the ideXlab platform.
-
sobolev mappings degree homotopy classes and rational homology spheres
2012Co-Authors: Pawel Goldstein, Piotr HajlaszAbstract:In this paper we investigate the degree and the homotopy theory of Orlicz–Sobolev mappings W 1,P (M,N) between manifolds, where the Young Function P satisfies a divergence condition and forms a slightly larger space than W 1,n , n=dim M. In particular, we prove that if M and N are compact oriented manifolds without boundary and dim M=dim N=n, then the degree is well defined in W 1,P (M,N) if and only if the universal cover of N is not a rational homology sphere, and in the case n=4, if and only if N is not homeomorphic to S 4.
-
sobolev mappings degree homotopy classes and rational homology spheres
2011Co-Authors: Pawel Goldstein, Piotr HajlaszAbstract:In the paper we investigate the degree and the homotopy theory of Orlicz-Sobolev mappings $W^{1,P}(M,N)$ between manifolds, where the Young Function $P$ satisfies a divergence condition and forms a slightly larger space than $W^{1,n}$, $n=\dim M$. In particular, we prove that if $M$ and $N$ are compact oriented manifolds without boundary and $\dim M=\dim N=n$, then the degree is well defined in $W^{1,P}(M,N)$ if and only if the universal cover of $N$ is not a rational homology sphere, and in the case $n=4$, if and only if $N$ is not homeomorphic to $S^4$.
Pawel Goldstein - One of the best experts on this subject based on the ideXlab platform.
-
sobolev mappings degree homotopy classes and rational homology spheres
2012Co-Authors: Pawel Goldstein, Piotr HajlaszAbstract:In this paper we investigate the degree and the homotopy theory of Orlicz–Sobolev mappings W 1,P (M,N) between manifolds, where the Young Function P satisfies a divergence condition and forms a slightly larger space than W 1,n , n=dim M. In particular, we prove that if M and N are compact oriented manifolds without boundary and dim M=dim N=n, then the degree is well defined in W 1,P (M,N) if and only if the universal cover of N is not a rational homology sphere, and in the case n=4, if and only if N is not homeomorphic to S 4.
-
sobolev mappings degree homotopy classes and rational homology spheres
2011Co-Authors: Pawel Goldstein, Piotr HajlaszAbstract:In the paper we investigate the degree and the homotopy theory of Orlicz-Sobolev mappings $W^{1,P}(M,N)$ between manifolds, where the Young Function $P$ satisfies a divergence condition and forms a slightly larger space than $W^{1,n}$, $n=\dim M$. In particular, we prove that if $M$ and $N$ are compact oriented manifolds without boundary and $\dim M=\dim N=n$, then the degree is well defined in $W^{1,P}(M,N)$ if and only if the universal cover of $N$ is not a rational homology sphere, and in the case $n=4$, if and only if $N$ is not homeomorphic to $S^4$.
Shravan N Kumar - One of the best experts on this subject based on the ideXlab platform.
-
optimal extension of the fourier transform and convolution operator on compact groups
2020Co-Authors: Manoj Kumar, Shravan N KumarAbstract:Abstract Let G be a compact group (not necessarily abelian) and let Φ be a Young Function satisfying the Δ 2 -condition. We determine the optimal domain and the associated extended operator for both Fourier transform and the convolution operator defined on the Orlicz spaces L Φ ( G ) .
-
optimal extension of the fourier transform and convolution operator on compact groups
2019Co-Authors: Manoj Kumar, Shravan N KumarAbstract:Let $G$ be a compact group (not necessarily abelian) and let $\Phi$ be a Young Function satisfying the $\Delta_2$-condition. We determine the optimal domain and the associated extended operator for both Fourier transform and the convolution operator defined on the Orlicz spaces $L^\Phi(G).$
Manoj Kumar - One of the best experts on this subject based on the ideXlab platform.
-
optimal extension of the fourier transform and convolution operator on compact groups
2020Co-Authors: Manoj Kumar, Shravan N KumarAbstract:Abstract Let G be a compact group (not necessarily abelian) and let Φ be a Young Function satisfying the Δ 2 -condition. We determine the optimal domain and the associated extended operator for both Fourier transform and the convolution operator defined on the Orlicz spaces L Φ ( G ) .
-
optimal extension of the fourier transform and convolution operator on compact groups
2019Co-Authors: Manoj Kumar, Shravan N KumarAbstract:Let $G$ be a compact group (not necessarily abelian) and let $\Phi$ be a Young Function satisfying the $\Delta_2$-condition. We determine the optimal domain and the associated extended operator for both Fourier transform and the convolution operator defined on the Orlicz spaces $L^\Phi(G).$
Theresa M. Offwood - One of the best experts on this subject based on the ideXlab platform.
-
A description of Banach space-valued Orlicz hearts
2010Co-Authors: Coenraad C.a. Labuschagne, Theresa M. OffwoodAbstract:Let Y be a Banach space, (Ω, Σ; μ) a probability space and φ a finite Young Function. It is shown that the Y-valued Orlicz heart Hφ(μ, Y) is isometrically isomorphic to the l-completed tensor product \( H_\varphi \left( \mu \right)\tilde \otimes _l Y \) of the scalar-valued Orlicz heart Hφ(μ) and Y, in the sense of Chaney and Schaefer. As an application, a characterization is given of the equality of \( \left( {H_\varphi \left( \mu \right)\tilde \otimes _l Y} \right)* \) and \( H_\varphi \left( \mu \right)*\tilde \otimes _l Y* \) in terms of the Radon-Nikodým property on Y. Convergence of norm-bounded martingales in Hφ(μ, Y) is characterized in terms of the Radon-Nikodým property on Y. Using the associativity of the l-norm, an alternative proof is given of the known fact that for any separable Banach lattice E and any Banach space Y, E and Y have the Radon-Nikodým property if and only if \( E\tilde \otimes _l Y \) has the Radon-Nikodým property. As a corollary, the Radon-Nikodým property in Hφ(μ, Y) is described in terms of the Radon-Nikodým property on Hφ(μ) and Y.
