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Derivatives of harmonic mixed norm and bloch-type spaces in the unit ball of R |
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| Authors: | Tang Xiaomin Hu Zhangjian |
| Affiliation: | a Department of Mathematics, University of Science and Technology of China, Hefei 230026, China b Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China c Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China d Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China |
| Abstract: | Let H(B) be the set of all harmonic functions f on the unit ball B of Rn. For 0 < p, q ≤ ∞ and a normal weight φ, the mixed norm space Hp,q, φ(B) consists of all functions f in H(B) for which the mixed norm p,q, φ < ∞. In this article, we obtain some characterizations in terms of radial, tangential, and partial derivative norms in Hp,q, φ(B). The parallel results for the Bloch-type space are also obtained. As an application, the analogous problems for polyharmonic functions are discussed. |
| Keywords: | Harmonic function mixed norm space Bloch-type space norm derivatives |
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