On some subspaces of Morrey-Sobolev spaces and boundedness of Riesz integrals

Mouhamadou Dosso, Ibrahim Fofana, and Moumine Sanogo. "On some subspaces of Morrey-Sobolev spaces and boundedness of Riesz integrals." Annales Polonici Mathematici 108.2 (2013): 133-153. <http://eudml.org/doc/280617>.

@article{MouhamadouDosso2013,
abstract = {For 1 ≤ q ≤ α ≤ p ≤ ∞, $(L^q,l^p)^\{α\}$ is a complex Banach space which is continuously included in the Wiener amalgam space $(L^q,l^p)$ and contains the Lebesgue space $L^\{α\}$. We study the closure $(L^q,l^p)^\{α\}_\{c,0\}$ in $(L^q,l^p)^\{α\}$ of the space of test functions (infinitely differentiable and with compact support in $ℝ^d$) and obtain norm inequalities for Riesz potential operators and Riesz transforms in these spaces. We also introduce the Sobolev type space $W¹((L^q,l^p)^\{α\})$ (a subspace of a Morrey-Sobolev space, but a superspace of the classical Sobolev space $W^\{1,α\}$) and obtain in it Sobolev inequalities and a Kondrashov-Rellich compactness theorem.},
author = {Mouhamadou Dosso, Ibrahim Fofana, Moumine Sanogo},
journal = {Annales Polonici Mathematici},
keywords = {amalgam space; Sobolev space; Riesz potential operator; Riesz transform},
language = {eng},
number = {2},
pages = {133-153},
title = {On some subspaces of Morrey-Sobolev spaces and boundedness of Riesz integrals},
url = {http://eudml.org/doc/280617},
volume = {108},
year = {2013},
}

TY - JOUR
AU - Mouhamadou Dosso
AU - Ibrahim Fofana
AU - Moumine Sanogo
TI - On some subspaces of Morrey-Sobolev spaces and boundedness of Riesz integrals
JO - Annales Polonici Mathematici
PY - 2013
VL - 108
IS - 2
SP - 133
EP - 153
AB - For 1 ≤ q ≤ α ≤ p ≤ ∞, $(L^q,l^p)^{α}$ is a complex Banach space which is continuously included in the Wiener amalgam space $(L^q,l^p)$ and contains the Lebesgue space $L^{α}$. We study the closure $(L^q,l^p)^{α}_{c,0}$ in $(L^q,l^p)^{α}$ of the space of test functions (infinitely differentiable and with compact support in $ℝ^d$) and obtain norm inequalities for Riesz potential operators and Riesz transforms in these spaces. We also introduce the Sobolev type space $W¹((L^q,l^p)^{α})$ (a subspace of a Morrey-Sobolev space, but a superspace of the classical Sobolev space $W^{1,α}$) and obtain in it Sobolev inequalities and a Kondrashov-Rellich compactness theorem.
LA - eng
KW - amalgam space; Sobolev space; Riesz potential operator; Riesz transform
UR - http://eudml.org/doc/280617
ER -