Maximal Weak-Type Inequality for Orthogonal Harmonic Functions and Martingales

• Autorzy: Osękowski A.

Identyfikatory

DOI

10.4064/ba61-3-3

• Języki publikacji: EN

Abstrakty

EN

Assume that u, v are conjugate harmonic functions on the unit disc of C, normalized so that u(0)=v(0)=0. Let u∗, |v|∗ stand for the one- and two-sided Brownian maxima of u and v, respectively. The paper contains the proof of the sharp weak-type estimate... [formula]. Actually, this estimate is shown to be true in the more general setting of differentially subordinate harmonic functions defined on Euclidean domains. The proof exploits a novel estimate for orthogonal martingales satisfying differential subordination.

Słowa kluczowe

EN

harmonic; martingale; maximal; weak type inequality; best constants

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2013
• Tom: Vol. 61, no 3-4
• Strony: 209--218
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Osękowski A.

• Department of Mathematics, Informatics and Mechanics University of Warsaw Banacha 2 02-097 Warszawa, Poland

Bibliografia

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