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A Note on Certain Block Spaces on the Unit Sphere

Authors:	Xiao Feng Ye Xiang Rong Zhu

Institution:	(1) Department of Mathematics (Xixi Campus), Zhejiang University, Hangzhou 310028, P. R. China

Abstract:	In this note, we clarify a relation between block spaces and the Hardy space. We obtain that block spaces $B^{{0,\nu }}_{q} {\left( {S^{{n - 1}} } \right)} \subset H^{1} {\left( {S^{{n - 1}} } \right)} + L{\left( {\ln ^{ + } L} \right)}^{{1 + \nu }} {\left( {S^{{n - 1}} } \right)},\nu > - 1,q > 1.$ Furthermore, if ν ≥ 0, q>1, we verify that block spaces $B^{{0,\nu }}_{q} {\left( {S^{{n - 1}} } \right)}$ are proper subspaces of H ¹(S ⁿ⁻¹). Project supported by 973–project (G1999075105), NSFC(G10271107), RFDP(20030335019) and ZJNSF (RC97017)

Keywords:	block spaces Hardy space
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