Maximal Functions at Infinity for Poisson Integrals on N A

Andrzej Hulanicki
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Andrzej Hulanicki: Wrocław University, Institute of Mathematics

A chapter in Harmonic Analysis and Discrete Potential Theory, 1992, pp 15-22 from Springer

Abstract: Abstract Let G be a Lie group, || · || a euclidean norm in the Lie algebra of G and || x || the corresponding riemannian distance of x to the identity in G. We say that a function f on G satisfies the right Hölder condition, if 1.1 % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qadaWdbaWdaeaapeGaaiiFaiaadAgacaGGOaGaamiEaiaadIgacaGG % PaGaeyOeI0IaamOzaiaacIcacaWG4bGaaiykaiaacYhaaSqabeqani % abgUIiYdGccaWGKbGaamiEaiabgsMiJkaadoeacaGG8bGaaiiFaiaa % dIgacaGG8bGaaiiFa8aadaahaaWcbeqaa8qacqaHXoqyaaGccaGGSa % GaeqySdeMaeyOpa4JaaGimaiaac6caaaa!529C! $$\int {|f(xh) - f(x)|} dx \leqslant C||h|{|^\alpha },\alpha > 0.$$ .

Keywords: Maximal Function; Weak Type; Harnack Inequality; Holder Condition; Fractional Moment (search for similar items in EconPapers)
Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4899-2323-3_2

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DOI: 10.1007/978-1-4899-2323-3_2

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