Volume integral means of holomorphic functions

DOI10.1090/S0002-9939-2010-10797-9zbMath1215.32002OpenAlexW2018446893MaRDI QIDQ2997204

Jie Xiao, K. H. Zhu

Publication date: 6 May 2011

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-2010-10797-9

zbMATH Keywords

monotonicitylogarithmic convexityBergman/Hardy spacesisoperimetric-type inequalitiesvolume/area integral meansweighted Ricci curvatures

Mathematics Subject Classification ID

(H^p)-spaces, Nevanlinna spaces of functions in several complex variables (32A35) Length, area and volume in real or complex geometry (51M25) Bergman spaces of functions in several complex variables (32A36) Holomorphic functions of several complex variables (32A10)

Related Items

Volume integral means over spherical shell ⋮ Schwarz lemma at the boundary on the classical domain of type \(\mathcal{II}\) ⋮ Hadamard convolution and area integral means in Bergman spaces ⋮ Bergman-Hölder functions, area integral means and extremal problems ⋮ Volterra-type operators on the minimal Möbius-invariant space ⋮ INTEGRAL MEANS OF HOLOMORPHIC FUNCTIONS AS GENERIC LOG-CONVEX WEIGHTS ⋮ Convexity properties of area integral means over the annuli ⋮ Convexity for area integral means ⋮ Convexity of area integral means for analytic functions ⋮ Hadamard products in weighted Bergman spaces ⋮ Mean Lipschitz conditions on Bergman space ⋮ Gaussian integral means of entire functions ⋮ Area integral means over the annuli ⋮ LOGARITHMIC CONVEXITY OF AREA INTEGRAL MEANS FOR ANALYTIC FUNCTIONS II ⋮ Upper and lower estimates for the modulus of bounded holomorphic functions ⋮ Growth and monotonicity properties for elliptically schlicht functions ⋮ Schwarz lemma at the boundary on the classical domain of type \(\mathcal{IV}\) ⋮ Convexities of Gaussian integral means and weighted integral means for analytic functions ⋮ Isoperimetry for semilinear torsion problems in Riemannian two-manifolds ⋮ Contractive inequalities for mixed norm spaces and the beta function ⋮ Hyperbolic geometric versions of Schwarz’s lemma ⋮ Addendum to ``Gaussian integral means of entire functions

Cites Work

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• New proofs of the isoperimetric inequality and some generalizations
• On strictly pseudoconvex domains with Kähler-Einstein Bergman metrics
• Area inequality and \(Q_{p}\) norm
• Sharp inequalities for holomorphic functions
• A new variant of the Schwarz-Pick-Ahlfors lemma
• Strictly pseudoconvex domains in 𝐶ⁿ
• Area, capacity and diameter versions of Schwarz’s Lemma
• The Isoperimetric Inequality and a Theorem of Hardy and Littlewood
• Translating Inequalities between Hardy and Bergman Spaces
• Spaces of Holomorphic Functions in the Unit Ball
• A Sharp Estimate for A p α Functions in C n
• Curvature and complex analysis
• New Proofs of Some Theorems of Hardy by Banach Space Methods