Weighted-Hardy functions with Hadamard gaps on the unit ball |
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Authors: | Songxiao Li Stevo Stevi? |
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Institution: | a Department of Mathematics, JiaYing University, 514015 Meizhou, GuangDong, China b Mathematical Institute of the Serbian Academy of Science, Knez Mihailova 36/III, 11000 Beograd, Serbia |
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Abstract: | We prove that an analytic function f on the unit ball B with Hadamard gaps, that is, (the homogeneous polynomial expansion of f) satisfying nk+1/nk?λ>1 for all k∈N, belongs to the space if and only if . Moreover, we show that the following asymptotic relation holds . Also we prove that limr→1(1-r2)α‖Rfr‖p=0 if and only if . These results confirm two conjectures from the following recent paper S. Stevi?, On Bloch-type functions with Hadamard gaps, Abstr. Appl. Anal. 2007 (2007) 8 pages (Article ID 39176)]. |
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Keywords: | Holomorphic function _method=retrieve& _eid=1-s2 0-S0096300309001374& _mathId=si10 gif& _pii=S0096300309001374& _issn=00963003& _acct=C000051805& _version=1& _userid=1154080& md5=72a1c29abe6cae4c5a684887bfcea39b')" style="cursor:pointer α-Bloch space" target="_blank">" alt="Click to view the MathML source" title="Click to view the MathML source">α-Bloch space Weighted-Hardy space Hadamard gaps Unit ball |
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