Lipschitz-type conditions on homogeneous Banach spaces of analytic functions

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作者：Oscar Blasco^a ; ¹ ; ^{oblasco@uv.es" class="auth_mail" title="E-mail the corresponding author} ; Georgios Stylogiannis^b ; ^{stylog@math.auth.gr" class="auth_mail" title="E-mail the corresponding author} ; ^{g.stylog@gmail.com" class="auth_mail" title="E-mail the corresponding author}
关键词：Banach spaces ; Lipschitz-type conditions ; Approximation by partial sums
刊名：Journal of Mathematical Analysis and Applications
出版年：2017
出版时间：1 January 2017
年：2017
卷：445
期：1
页码：612-630
全文大小：387 K

文摘

In this paper we deal with Banach spaces of analytic functions m>X m> defined on the unit disk satisfying that mmlsi1" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16304012&_mathId=si1.gif&_user=111111111&_pii=S0022247X16304012&_rdoc=1&_issn=0022247X&md5=9e41b59e0d39d55b3e17c56f5a20b3f0" title="Click to view the MathML source">R_tf∈XmathContainer hidden">mathCode"><math altimg="si1.gif" overflow="scroll"><msub><mrow><mi>Rmi>mrow><mrow><mi>tmi>mrow>msub><mi>fmi><mo>∈mo><mi>Xmi>math> for any mmlsi2" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16304012&_mathId=si2.gif&_user=111111111&_pii=S0022247X16304012&_rdoc=1&_issn=0022247X&md5=653e962132a2a043da43c6f2e2e862fd" title="Click to view the MathML source">t>0mathContainer hidden">mathCode"><math altimg="si2.gif" overflow="scroll"><mi>tmi><mo>>mo><mn>0mn>math> and mmlsi3" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16304012&_mathId=si3.gif&_user=111111111&_pii=S0022247X16304012&_rdoc=1&_issn=0022247X&md5=7cce2c1e426ebd5343134f03376773ba" title="Click to view the MathML source">f∈XmathContainer hidden">mathCode"><math altimg="si3.gif" overflow="scroll"><mi>fmi><mo>∈mo><mi>Xmi>math>, where mmlsi4" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16304012&_mathId=si4.gif&_user=111111111&_pii=S0022247X16304012&_rdoc=1&_issn=0022247X&md5=d3b24d9a9134cf0350e164af3f95adce" title="Click to view the MathML source">R_tf(z)=f(e^itz)mathContainer hidden">mathCode"><math altimg="si4.gif" overflow="scroll"><msub><mrow><mi>Rmi>mrow><mrow><mi>tmi>mrow>msub><mi>fmi><mo stretchy="false">(mo><mi>zmi><mo stretchy="false">)mo><mo>=mo><mi>fmi><mo stretchy="false">(mo><msup><mrow><mi>emi>mrow><mrow><mi>imi><mi>tmi>mrow>msup><mi>zmi><mo stretchy="false">)mo>math>. We study the space of functions in m>X m> such that mmlsi5" class="mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16304012&_mathId=si5.gif&_user=111111111&_pii=S0022247X16304012&_rdoc=1&_issn=0022247X&md5=df60d8b0f633c3b9ac9117bb542a8bb6">mg class="imgLazyJSB inlineImage" height="22" width="174" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022247X16304012-si5.gif">

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