Extension theorems for real variable Hardy and Hardy-Sobolev spaces

  • Akihiko Miyachi
Conference paper


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 \( H_{p}^{k}({R^{n}}) \) 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 \( H_{p}^{k}({R^{n}}) \) only for k n/p-n.


Maximal Function Extension Theorem Dyadic Cube Euclidean Domain Pointwise Inequality 
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Copyright information

© Springer-Verlag Tokyo 1991

Authors and Affiliations

  • Akihiko Miyachi
    • 1
  1. 1.Department of MathematicsHitotsubashi UniversityKunitachi, TokyoJapan

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