More properties of weighted Berezin transform in the unit ball of $\mathbb C^n$
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초록
We exhibit various properties of the weighted Berezin operator $T_{\alpha}$ and its iteration $T_{\alpha}^{k}$ on $L^{p}(\tau)$, where $\alpha > -1$ and $\tau$ is the invariant measure on the complex unit ball $B_n$. Iterations of $T_{\alpha}$ on $L^{1}_{R}(\tau)$ the space of radial integrable functions have performed important roles in proving $\mathcal{M}$-harmonicity of bounded functions with invariant mean value property. We show differences between the case of $1<p<\infty$ and $p=1, \infty$ under the infinite iteration of $T_{\alpha}$ or the infinite summation of iterations, most of which are extensions or related assertions to the propositions of the previous results.
Abstract
We exhibit various properties of the weighted Berezin operator $T_{\alpha}$ and its iteration $T_{\alpha}^{k}$ on $L^{p}(\tau)$, where $\alpha > -1$ and $\tau$ is the invariant measure on the complex unit ball $B_n$. Iterations of $T_{\alpha}$ on $L^{1}_{R}(\tau)$ the space of radial integrable functions have performed important roles in proving $\mathcal{M}$-harmonicity of bounded functions with invariant mean value property. We show differences between the case of $1<p<\infty$ and $p=1, \infty$ under the infinite iteration of $T_{\alpha}$ or the infinite summation of iterations, most of which are extensions or related assertions to the propositions of the previous results.
참고문헌 (7)
- P. Ahern, "An invariant volume-mean-value property", J. Funct. Anal, 111(2), pp.380~397 (1993)
- H. Furstenberg, "A Poisson formula for semi-simple Lie groups", Ann. of Math, 77(2), pp.335~386 (1963)
- H. Furstenberg, "Boundaries of Riemannian symmetric spaces, Symmetric spaces", Washington Univ, ~ (1969)
- J. Lee., "Weighted Berezin transform in the polydisc", J. Math. Anal. Appl, 338(2), pp.1489~1493 (2008)
- 이재성, "A CHARACTERIZATION OF M-HARMONICITY", 대한수학회보, 47(1), pp.113~119 (2010), 대한수학회
- 이재성, "Iterates of weighted Berezin transform under invariant measure in the unit ball", 한국수학논문집, 28(3), pp.449~457 (2020), 강원경기수학회
- W. Rudin, "Function theory in the unit ball of C n" (1980), Springer-Verlag