Strong \(L^ p\) estimates for maximal functions with respect to singular measures; with applications to exceptional sets

DOI10.1215/S0012-7094-86-05323-8zbMath0601.32007OpenAlexW2005587510MaRDI QIDQ1080989

Patrick Ahern, Alexander Nagel

Publication date: 1986

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-86-05323-8

zbMATH Keywords

area integralspaces of homogeneous typemaximal functionsapproach regionexceptional sets\(L^ p\)- boundednessboundary behavior of holomorphic and harmonic functions

Mathematics Subject Classification ID

(H^p)-spaces, Nevanlinna spaces of functions in several complex variables (32A35) Boundary behavior of holomorphic functions of several complex variables (32A40) Potentials and capacities on other spaces (31C15)

Related Items

Area integral associated with singular measures on the unit sphere on \(\mathbb{C}^ n\) ⋮ Tangential boundary limits and exceptional sets for holomorphic functions in Dirichlet-type spaces ⋮ Interpolation along manifolds in Hardy-Sobolev spaces ⋮ Weighted weak-type inequalities for the maximal function of nonnegative integral transforms over approach regions ⋮ A characterisation of tangential exceptional sets for αp = n ⋮ Tangential boundary behavior of functions of several variables ⋮ Boundary Tangential Convergence on Spaces of Homogeneous Type ⋮ Poisson integrals of Bessel potentials

Cites Work

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• Tangential boundary behavior of functions in Dirichlet-type spaces
• On certain maximal functions and approach regions
• On the boundary limits of harmonic functions with gradient in \(L^p\)
• The Lindelöf principle and normal functions of several complex variables
• Some new function spaces and their applications to harmonic analysis.
• Analyse harmonique non-commutative sur certains espaces homogènes. Etude de certaines intégrales singulières. (Non-commutative harmonic analysis on certain homogeneous spaces. Study of certain singular integrals.)
• Angular and Tangential Limits of Blaschke Products and their Successive Derivatives
• Tangential Limits of Functions of the Class S α
• Local Boundary Behavior of Bounded Holomorphic Functions
• Imbedding theorems of Sobolev type in potential theory.
• Harmonic Functions on Hermitian Hyperbolic Space
• Boundary Behavior of Holomorphic Functions of Several Complex Variables. (MN-11)