On the singular values of compact composition operators
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Let μ   be a positive Borel measure on the unit disc and let rc">rmulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1631073X16301881&_mathId=si1.gif&_user=111111111&_pii=S1631073X16301881&_rdoc=1&_issn=1631073X&md5=7982e1ec796f2dc0cf2c1fe7efb5d2f3" title="Click to view the MathML source">Tμr hidden">rflow="scroll">row>Trow>row>μrow> be the associated Toeplitz operator on a standard Bergman space. Under some convexity conditions on a positive function h  , we give an upper and lower bounds of the trace of rc">rmulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1631073X16301881&_mathId=si2.gif&_user=111111111&_pii=S1631073X16301881&_rdoc=1&_issn=1631073X&md5=53e2d7751487b8990d87e02557f18a08" title="Click to view the MathML source">h(Tμ)r hidden">rflow="scroll">hretchy="false">(row>Trow>row>μrow>retchy="false">). As consequence, we give some asymptotic estimates of eigenvalues of rc">rmulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1631073X16301881&_mathId=si1.gif&_user=111111111&_pii=S1631073X16301881&_rdoc=1&_issn=1631073X&md5=7982e1ec796f2dc0cf2c1fe7efb5d2f3" title="Click to view the MathML source">Tμr hidden">rflow="scroll">row>Trow>row>μrow>. We also apply these results to composition operators and give some concrete examples.

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