On the boundedness of operators in \(L^p(l^q)\) and Triebel--Lizorkin spaces (Q935642)
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scientific article; zbMATH DE number 5310051
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the boundedness of operators in \(L^p(l^q)\) and Triebel--Lizorkin spaces |
scientific article; zbMATH DE number 5310051 |
Statements
On the boundedness of operators in \(L^p(l^q)\) and Triebel--Lizorkin spaces (English)
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12 August 2008
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Summary: Given a bounded linear operator \(T:L^{p_0}(\mathbb R^n)\to L^{p_1}(\mathbb R^n)\), for \(1\leq p_0,p_1\leq\infty\), we state conditions under which \(T\) defines a bounded operator between corresponding pairs of \(L^p(\mathbb R^n;l^q)\) spaces and Triebel--Lizorkin spaces \(F_{p,q}^s(\mathbb R^n)\). Applications are given to linear parabolic equations and to Schrödinger semigroups.
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