Extension theorems for real variable Hardy and Hardy-Sobolev spaces
For 0 < p ≤1, let Hp(Rn) denote the real variable Hardy space as given in the paper of C. Fefferrnan and E. M. Stein [2; Section 11]. For 0< p≤ 1 and k ∈ N (= the set of positive integers), we define \(
\) as the set of the distributions f on Rn for which the derivatives ∂αf belong to Hp(Rn) for |α| = k. (Contrary to the custom, we do not require ∂αf ∈ Hp (Rn) for |α| k.) We shall consider \(
\) only for k n/p-n.
KeywordsMaximal Function Extension Theorem Dyadic Cube Euclidean Domain Pointwise Inequality
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