LITTLE HANKEL OPERATORS ON WEIGHTED BLOCH SPACES IN Cn

Title & Authors
LITTLE HANKEL OPERATORS ON WEIGHTED BLOCH SPACES IN Cn
Choi, Ki-Seong;

Abstract
Let B be the open unit ball in $\small{C^{n}}$ and $\small{{\mu}_{q}}$(q > -1) the Lebesgue measure such that $\small{{\mu}_{q}}$(B) ＝ 1. Let $\small{{L_{a,q}}^2}$ be the subspace of $\small{{L^2(B,D{\mu}_q)}$ consisting of analytic functions, and let $\small{\overline{{L_{a,q}}^2}}$ be the subspace of $\small{{L^2(B,D{\mu}_q)}$) consisting of conjugate analytic functions. Let $\small{\bar{P}}$ be the orthogonal projection from $\small{{L^2(B,D{\mu}_q)}$ into $\small{\overline{{L_{a,q}}^2}}$. The little Hankel operator $\small{{h_{\varphi}}^{q}\;:\;{L_{a,q}}^2\;{\rightarrow}\;{\overline}{{L_{a,q}}^2}}$ is defined by ${h_{\varphi}}^{q}(\cdot)\; Keywords Bergman space;little Hankel operator;weighted Bloch space; Language English Cited by 1. NOTES ON THE BERGMAN PROJECTION TYPE OPERATOR IN ℂn,; 대한수학회논문집, 2006. vol.21. 1, pp.65-74 2. NOTES ON CARLESON TYPE MEASURES ON BOUNDED SYMMETRIC DOMAIN,; 대한수학회논문집, 2007. vol.22. 1, pp.65-74 3. ON SOME MEASURE RELATED WITH POISSON INTEGRAL ON THE UNIT BALL,;; 충청수학회지, 2009. vol.22. 1, pp.89-99 4. ON DUALITY OF WEIGHTED BLOCH SPACES IN${\mathbb{C}}^n$,;; 충청수학회지, 2010. vol.23. 3, pp.523-534 5. SOME RESULTS RELATED WITH POISSON-SZEG$\ddot{O}$KERNEL AND BEREZIN TRANSFORM,;; 충청수학회지, 2011. vol.24. 3, pp.417-426 6. BLOCH-TYPE SPACE RELATED WITH NORMAL FUNCTION,; 충청수학회지, 2011. vol.24. 3, pp.533-541 7. NOTES ON THE SPACE OF DIRICHLET TYPE AND WEIGHTED BESOV SPACE,; 충청수학회지, 2013. vol.26. 2, pp.393-402 8. TOEPLITZ TYPE OPERATOR IN ℂn,; 충청수학회지, 2014. vol.27. 4, pp.697-705 1. NOTES ON THE SPACE OF DIRICHLET TYPE AND WEIGHTED BESOV SPACE, Journal of the Chungcheong Mathematical Society , 2013, 26, 2, 393 2. TOEPLITZ TYPE OPERATOR IN ℂn, Journal of the Chungcheong Mathematical Society , 2014, 27, 4, 697 3. NOTES ON${\alpha}$-BLOCH SPACE AND$D_p({\mu})$, Journal of the Chungcheong Mathematical Society , 2012, 25, 3, 543 References 1. Amer. J. Math., 1988. vol.110. pp.989-1054 2. Duke Math. J., 0000. vol.53. pp.315-332 3. Amer. J. Math., 1988. vol.110. pp.921-953 4. J. Funct. Anal., 1990. vol.93. pp.310-350 5. J. Korean Math. Soc., 1998. vol.35. pp.171-189 6. Revista Math. Ibero-amer, 1987. vol.3. pp.61-138 7. Function theory in the unit ball of$\mathbb{C}^ n\$, 1980.

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