The Banach envelopes of Besov and Triebel-Lizorkin spaces and applications to partial differential equations
نویسندگان
چکیده
With “hat” denoting the Banach envelope (of a quasi-Banach space) we prove that ̂ B p (Rn) = B s−n ( 1 p −1 ) ,1 1 (R ), ̂ F s,q p (Rn) = B s−n ( 1 p −1 ) ,1 1 (R ), if 0 < p < 1, 0 < q < 1, s ∈ R, while ̂ B p (Rn) = B s−n ( 1 p −1 ) ,q 1 (R ), ̂ F s,q p (Rn) = B s−n ( 1 p −1 ) ,1 1 (R ), if 0 < p < 1, 1 ≤ q < +∞, s ∈ R, and ̂ B p (Rn) = B p (R), ̂ F s,q p (Rn) = F s,1 p (R), if 1 ≤ p < +∞, 0 < q < 1, s ∈ R. Applications to questions regarding the global interior regularity of solutions to Poisson type problems for the three-dimensional Lamé system in Lipschitz domains are presented.
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