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We focus on the interations of the weighted Berezin transform $T_{\alpha}$ on $L^{p}(\tau)$, where $\tau$ 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 played important roles in proving $\mathcal{M}$-harmonicity of bounded functions with invariant mean value property. Here, we introduce more properties on iterations of $T_{\alpha}$ on $L^{1}_{R}(\tau)$ and observe differences between the iterations of $T_{\alpha}$ on $L^{1}(\tau)$ and $L^{p}(\tau)$ for $1<p<\infty$.
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참고문헌 (7)
참고문헌 신청
P. Ahern / 1993 / An invariant volume-mean-value property / J. Funct. Anal 111(2):380~397
H. Furstenberg / 1963 / A Poisson formula for semi-simple Lie groups / Ann. of Math 77(2):335~386
H. Furstenberg / 1969 / Boundaries of Riemannian symmetric spaces, Symmetric spaces
J. Lee / 2008 / Weighted Berezin transform in the polydisc / J. Math. Anal. Appl 338(2):1489~1493
이재성 / 2010 / A CHARACTERIZATION OF M-HARMONICITY / 대한수학회보 47(1):113~119
H. Furstenberg / 1963 / A Poisson formula for semi-simple Lie groups / Ann. of Math 77(2):335~386
H. Furstenberg / 1969 / Boundaries of Riemannian symmetric spaces, Symmetric spaces
J. Lee / 2008 / Weighted Berezin transform in the polydisc / J. Math. Anal. Appl 338(2):1489~1493
이재성 / 2010 / A CHARACTERIZATION OF M-HARMONICITY / 대한수학회보 47(1):113~119
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