Analytic potential theory over the \(p\)-adics

DOI10.5802/aif.1361zbMath0847.31006OpenAlexW2068282595MaRDI QIDQ1318002

Shai M. J. Haran

Publication date: 21 February 1996

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_1993__43_4_905_0

zbMATH Keywords

regularizationconvexitybalayageDirichlet problemsequilibrium measuredominationlocal fielddescentdichotomy\(\alpha\)-harmonic functionsRiesz potentialsRiesz representationGreen measure\(\alpha\)-superharmonic functions\(\alpha\)-capacity\(\alpha\)-homogeneous distributionsanalytic potential theoryfinite energy measuresharmonic minorantKeldish transformuniqueness principle

Mathematics Subject Classification ID

Measures on groups and semigroups, etc. (43A05) Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) Potentials and capacities on other spaces (31C15) Non-Archimedean function theory (30G06) Other generalizations (nonlinear potential theory, etc.) (31C45) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

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Besov space and trace theorem on a local field and its application ⋮ Carleson measures and the BMO space on the p -adic vector space ⋮ Estimates of weighted Hardy--Littlewood averages on the \(p\)-adic vector space ⋮ Estimates for \(p\)-adic fractional integral operator and its commutators on \(p\)-adic Morrey-Herz spaces ⋮ The \(p\)-adic weighted Hardy-Cesàro operators on weighted Morrey-Herz space ⋮ Weighted Hardy-Littlewood operators and commutators on \(p\)-adic functional spaces ⋮ \(p\)-adic mathematical physics: the first 30 years ⋮ Weighted inequalities for commutators of \(p\)-adic Hausdorff operators on Herz spaces ⋮ \(p\)-adic Riesz potential and its commutators on Morrey-Herz spaces ⋮ The Vladimirov-Taibleson operator: inequalities, Dirichlet problem, boundary Hölder regularity ⋮ Weak and strong boundedness for \(p\)-adic fractional Hausdorff operator and its commutator ⋮ Some estimates for \(p\)-adic rough multilinear Hausdorff operators and commutators on weighted Morrey-Herz type spaces ⋮ Sharp estimates of \(p\)-adic Hardy and Hardy-Littlewood-Pólya operators ⋮ Unnamed Item ⋮ Boundedness of \(p\)-adic Hardy operators and their commutators on \(p\)-adic central Morrey and BMO spaces ⋮ Riesz potentials and explicit sums in arithmetic ⋮ Hardy-Littlewood-Sobolev inequalities on \(p\)-adic central Morrey spaces ⋮ Gibbs phenomenon for Fourier partial sums on \(\mathbb{Z}_p\) ⋮ Parabolic equations and Markov processes over \(p\)-adic fields ⋮ Weak solutions of stochastic differential equations over the field of \(p\)-adic numbers ⋮ A lift of spatially inhomogeneous Markov process to extensions of the field of \(p\)-adic numbers ⋮ On \(p\)-adic mathematical physics ⋮ Fractal theoretic aspects of local field ⋮ Sharp estimates of \(m\)-linear \(p\)-adic Hardy and Hardy-Littlewood-Pólya operators ⋮ \((r, p)\)-capacity and Hausdorff measure on a local field ⋮ Commutator of Riesz potential in \(p\)-adic generalized Morrey spaces ⋮ Weighted estimates for maximal operators, Riesz potential operators and commutators on \(p\)-adic Lebesgue and Morrey spaces ⋮ Weighted Lebesgue and central Morrey estimates for \(p\)-adic multilinear Hausdorff operators and their commutators ⋮ \(p\)-adic singular integrals and their commutators in generalized Morrey spaces ⋮ Heat kernels for isotropic-like Markov generators on ultrametric spaces: a survey ⋮ Some estimates for \(p\)-adic fractional integral operator and its commutators on \(p\)-adic Herz spaces with rough kernels ⋮ Quantizations and symbolic calculus over the \(p\)-adic numbers

Cites Work

• Markoff processes and potentials. I, II, III
• Riesz potentials and explicit sums in arithmetic
• Potential theory. An analytic and probabilistic approach to balayage
• Infinitely divisible processes and their potential theory. I
• Fourier Analysis on Local Fields. (MN-15)
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