On an integral-type operator from the Bloch space to mixed norm spaces

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• 作者：Hao Li ; ^{hnulihao2012@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Integral-type operator ; Mixed norm space ; Bloch space ; Boundedness ; Compactness
• 刊名：Applied Mathematics and Computation
• 出版年：2016
• 出版时间：15 January 2016
• 年：2016
• 卷：273
• 期：Complete
• 页码：624-630
• 全文大小：296 K

文摘

Let φ be a holomorphic self-map of B and g ∈ H(B  ) such that class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0096300315013648&_mathId=si1.gif&_user=111111111&_pii=S0096300315013648&_rdoc=1&_issn=00963003&md5=65bd7684051939447e787ebfa3bb28cb" title="Click to view the MathML source">g(0)=0,class="mathContainer hidden">class="mathCode">$g\left(0\right)=0,$ where H(B) is the space of all holomorphic functions on the unit ball B   of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0096300315013648&_mathId=si2.gif&_user=111111111&_pii=S0096300315013648&_rdoc=1&_issn=00963003&md5=b15d1409947227774fcb3b7e2a0021f3" title="Click to view the MathML source">nCclass="mathContainer hidden">class="mathCode">${\mathbb{C}}^n$. In this paper we investigate the following integral-type operatorwhere class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0096300315013648&_mathId=si4.gif&_user=111111111&_pii=S0096300315013648&_rdoc=1&_issn=00963003&md5=34d081b57376964f50a5766244c2a704" title="Click to view the MathML source">Dfclass="mathContainer hidden">class="mathCode">$\mathcal{D}f$ is the fractional derivative of f ∈ H(B  ). The boundedness and compactness of the operators class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0096300315013648&_mathId=si5.gif&_user=111111111&_pii=S0096300315013648&_rdoc=1&_issn=00963003&md5=210f7890491494a6a2532a65a0a11f50">class="imgLazyJSB inlineImage" height="21" width="23" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0096300315013648-si5.gif">class="mathContainer hidden">class="mathCode">${\mathcal{D}}_{\phi }^g$ between mixed norm spaces and Bloch spaces in the unit ball are studied.