文摘
The aim of this paper is to find weights W in the unit ball of pan id="mmlsi1" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16306217&_mathId=si1.gif&_user=111111111&_pii=S0022247X16306217&_rdoc=1&_issn=0022247X&md5=b67ac7089eb5557da12fb58642c7c30a" title="Click to view the MathML source">Cp>np>pan>pan class="mathContainer hidden">pan class="mathCode">pan>pan>pan> for which characterization of the area integrals of Bergman spaces pan id="mmlsi2" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16306217&_mathId=si2.gif&_user=111111111&_pii=S0022247X16306217&_rdoc=1&_issn=0022247X&md5=55a85cb45243a80e26bc7e5d7bcc5c3e" title="Click to view the MathML source">Ap>pp>(W)pan>pan class="mathContainer hidden">pan class="mathCode">pan>pan>pan> holds. The area functions, related to those used to describe Hardy spaces, involve the radial derivative, the complex gradient and the invariant gradient. We extend to certain Bekollé weights the characterization by Z. Chen and W. Ouyang of the Bergman spaces with the classical weights pan id="mmlsi3" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16306217&_mathId=si3.gif&_user=111111111&_pii=S0022247X16306217&_rdoc=1&_issn=0022247X&md5=9e9d73c2c9539b5ebafe15827dc8a2fe" title="Click to view the MathML source">W(z)=(1−|z|)p>αp>pan>pan class="mathContainer hidden">pan class="mathCode">pan>pan>pan> using area functions.