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The Mixed Norm Spaces of Polyharmonic Functions

Author： Hu Zhangjian Pavlović Miroslav Zhang Xuejun

Publisher： Springer Publishing Company

ISSN： 0926-2601

Source： Potential Analysis, Vol.27, Iss.2, 2007-09, pp. : 167-182

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

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Abstract

Let be a bounded domain with C ² boundary. And let H _k be the set of all polyharmonic functions f with order k on Ω. For 0<p, q≤∞ and Φ a normal weight, the mixed-norm space consists of all function f in H _k for which the mixed-norm ||·||_{p, q, Φ}<∞. The main result of the paper is the norm equivalence: where x ₀ is a fixed point in Ω, m is a positive integer and is the jth gradient of f. A similar result for Bloch-type spaces is also obtained.

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