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

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Dosso M., Fofana I., Sanogo M.

Annales Polonici Mathematici

2013

tom 108

nr 2

133-153

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 𝓓 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.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Dosso M.

1 Fofana I.

1 Sanogo M.

1 2013

Wyniki wyszukiwania

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