On the fractional integro-differentiation operator in \(\mathbb{R}^n\)

DOI10.3103/S1068362315050040zbMath1337.31010MaRDI QIDQ260370

Y. G. Tonoyan, K. L. Avetisian

Publication date: 21 March 2016

Published in: Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences (Search for Journal in Brave)

zbMATH Keywords

fractional derivativesharmonic functionsfractional integralsunit ball in \(\mathbb{R}^n\)

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Integral representations, integral operators, integral equations methods in higher dimensions (31B10)

Related Items

Estimates for harmonic reproducing kernel and Bergman type operators on mixed norm and Besov spaces in the real ball ⋮ Poisson-Bergman type operators on Lipschitz and mixed norm spaces in the real ball ⋮ Fractional integration in weighted Lebesgue spaces

Cites Work

• Weighted integrals and Bloch spaces of \(n\)-harmonic functions on the polydisc
• Reproducing kernels for harmonic Bergman spaces of the unit ball
• Continuous inclusions and Bergman type operators in \(n\)-harmonic mixed norm spaces on the polydisc
• \(L^p\) continuity of projectors of weighted harmonic Bergman spaces
• Harmonic Bergman functions on the unit ball in \(\mathbb R^n\)
• Continuous embeddings in harmonic mixed norm spaces on the unit ball in \(\mathbb{R}^n\)
• The dual of an inequality of Hardy and Littlewood and some related inequalities
• Lipschitz spaces of functions on the circle and the disc
• Harmonic Function Theory
• Mixed-Norm Generalizations of Bergman Spaces and Duality
• ON WEIGHTED HARMONIC BERGMAN SPACES
• Bounded projections and duality in mixed-norm spaces of analytic functions
• Weighted Harmonic Bloch Spaces and Gleason's Problem
• Spaces of Holomorphic Functions in the Unit Ball
• HOLOMORPHIC FUNCTIONS ON THE MIXED NORM SPACES ON THE POLYDISC
• On weighted classes of harmonic functions in the unit ball of R ⁿ
• THEOREMS CONCERNING MEAN VALUES OF ANALYTIC OR HARMONIC FUNCTIONS
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