대한수학회지 (Journal of the Korean Mathematical Society)

  • 제43권3호
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  • Pages.579-591
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  • 2006
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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A GENERALIZATION OF A RESULT OF CHOA ON ANALYTIC FUNCTIONS WITH HADAMARD GAPS

  • Stevic Stevo (Mathematical Institute of Serbian Academy of Science)
  • 발행 : 2006.05.01
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초록

In this paper we obtain a sufficient and necessary condition for an analytic function f on the unit ball B with Hadamard gaps, that is, for $f(z)\;=\;{\sum}^{\infty}_{k=1}\;P_{nk}(z)$ (the homogeneous polynomial expansion of f) satisfying $n_{k+1}/n_{k}{\ge}{\lambda}>1$ for all $k\;{\in}\;N$, to belong to the weighted Bergman space $$A^p_{\alpha}(B)\;=\;\{f{\mid}{\int}_{B}{\mid}f(z){\mid}^{p}(1-{\mid}z{\mid}^2)^{\alpha}dV(z) < {\infty},\;f{\in}H(B)\}$$. We find a growth estimate for the integral mean $$\({\int}_{{\partial}B}{\mid}f(r{\zeta}){\mid}^pd{\sigma}({\zeta})\)^{1/p}$$, and an estimate for the point evaluations in this class of functions. Similar results on the mixed norm space $H_{p,q,{\alpha}$(B) and weighted Bergman space on polydisc $A^p_{^{\to}_{\alpha}}(U^n)$ are also given.

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참고문헌

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  12. Sharp inclusions and lacunary series in mixed-norm spaces on the polydisc vol.58, pp.2, 2013, https://doi.org/10.1080/17476933.2011.561839