Exact location of \(\alpha\)-Bloch spaces in \(L^p_a\) and \(H^p\) of a complex unit ball

DOI10.1216/rmjm/1021477265zbMath0978.32002OpenAlexW2044558555MaRDI QIDQ5928730

Wei-Sheng Yang, Caiheng Ouyang

Publication date: 1 April 2001

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://math.la.asu.edu/~rmmc/rmj/VOL30-3/CONT30-3/CONT30-3.html

zbMATH Keywords

\(\alpha\)-Bloch spacesball algebraBergman spacesgrowth rate of gradientHardy spacespower series with Hadamard gapsradial derivativestrict and best possible inclusions

Mathematics Subject Classification ID

Bloch functions, normal functions of several complex variables (32A18) Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) (32A37) Linear function spaces and their duals (46E99)

Related Items (12)

Spaces \(M(\mathcal D_p),\mathcal B_n^p\) and \(\mathcal Q_p\) ⋮ The \(L^p\)-\(L^q\) boundedness and compactness of Bergman type operators ⋮ \(\alpha\)-Bloch functions and Lipschitz classes ⋮ Equivalent characterizations of \(\alpha\)-Bloch functions on the unit ball ⋮ WEIGHTED COMPOSITION OPERATORS FROM F(p, q, s) TO BLOCH TYPE SPACES ON THE UNIT BALL ⋮ Norm equivalence and composition operators between Bloch/Lipschitz spaces of the ball ⋮ Composition operators on \(\alpha\)-Bloch spaces of the unit ball ⋮ An estimate of the essential norm of a composition operator from \(F(p,q,s)\) to \(\mathcal B^\alpha \) in the unit ball ⋮ Inclusion relations between harmonic Bergman-Besov and weighted Bloch spaces on the unit ball ⋮ Bloch type spaces on the unit ball of a Hilbert space ⋮ Weighted composition operators of \(H ^{\infty }\) into \(\alpha \)-Bloch spaces on the unit ball ⋮ Characterizations of \(\alpha \)-Bloch functions on the unit ball without use of derivative

Cites Work

• Möbius invariant \(Q_p\) spaces associated with the Green's function on the unit ball of \(C^n\)
• Some properties of fractional integrals. II
• L p -Behavior of Power Series with Positive Coefficients and Hardy Spaces
• Bloch Functions in Several Complex Variables, I
• On Homogeneous Polynomials on a Complex Ball
• Functions in All H^p Spaces, p < ∞
• A property of analytic functions with Hadamard gaps
• Inequalities for the Integral Means of Holomorphic Functions and their Derivatives in the Unit Ball of C n
• Radial Divergence in BMOA
• Characterizations of Bergman Spaces and Bloch Space in the Unit Ball of C n
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