DOI QR코드

DOI QR Code

LITTLE HANKEL OPERATORS ON WEIGHTED BLOCH SPACES IN Cn

  • 발행 : 2003.07.01

초록

Let B be the open unit ball in $C^{n}$ and ${\mu}_{q}$(q > -1) the Lebesgue measure such that ${\mu}_{q}$(B) = 1. Let ${L_{a,q}}^2$ be the subspace of ${L^2(B,D{\mu}_q)$ consisting of analytic functions, and let $\overline{{L_{a,q}}^2}$ be the subspace of ${L^2(B,D{\mu}_q)$) consisting of conjugate analytic functions. Let $\bar{P}$ be the orthogonal projection from ${L^2(B,D{\mu}_q)$ into $\overline{{L_{a,q}}^2}$. The little Hankel operator ${h_{\varphi}}^{q}\;:\;{L_{a,q}}^2\;{\rightarrow}\;{\overline}{{L_{a,q}}^2}$ is defined by ${h_{\varphi}}^{q}(\cdot)\;=\;{\bar{P}}({\varphi}{\cdot})$. In this paper, we will find the necessary and sufficient condition that the little Hankel operator ${h_{\varphi}}^{q}$ is bounded(or compact).

키워드

참고문헌

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피인용 문헌

  1. TOEPLITZ TYPE OPERATOR IN ℂn vol.27, pp.4, 2014, https://doi.org/10.14403/jcms.2014.27.4.697
  2. NOTES ON THE SPACE OF DIRICHLET TYPE AND WEIGHTED BESOV SPACE vol.26, pp.2, 2013, https://doi.org/10.14403/jcms.2013.26.2.393
  3. NOTES ON ${\alpha}$-BLOCH SPACE AND $D_p({\mu})$ vol.25, pp.3, 2012, https://doi.org/10.14403/jcms.2012.25.3.543