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We define Bloch-type spaces of $\mathcal{C}^1(\IH)$ on the upper half plane $\mathbb{H}$ and characterize them in terms of weighted Lipschitz functions. We also discuss the boundedness of a composition operator $C_\phi$ acting between two Bloch spaces. These obtained results generalize the corresponding known ones to the setting of upper half plane.
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참고문헌 (21)
참고문헌 신청
P. Bourgrade / 2005 / Heat kernel espansion for a family of stochastic volatility models: δ-geometry / Comput. Res. Reposi :31~46
S. Chen / 2015 / On characterizations of Bloch-type, Hardy-type and Lipschitz-type spaces / Math Z 279(1-2):163~183
S. Chen / 2011 / On harmonic Bloch spaces in the unit ball of Cn / Bull. Aust. Math. Soc 84(1):67~78
B. R. Choe / 2011 / Double integral characterizations of harmonic Bergman spaces / J. Math. Anal. Appl 379(2):889~909
F. Colonna / 1989 / The Bloch constant of bounded harmonic mappings / Indiana Univ. Math. J 38(4):829~840
S. Chen / 2015 / On characterizations of Bloch-type, Hardy-type and Lipschitz-type spaces / Math Z 279(1-2):163~183
S. Chen / 2011 / On harmonic Bloch spaces in the unit ball of Cn / Bull. Aust. Math. Soc 84(1):67~78
B. R. Choe / 2011 / Double integral characterizations of harmonic Bergman spaces / J. Math. Anal. Appl 379(2):889~909
F. Colonna / 1989 / The Bloch constant of bounded harmonic mappings / Indiana Univ. Math. J 38(4):829~840
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