Sharp Weak-Type Inequality for the Haar System, Harmonic Functions and Martingales

• Autorzy: Osękowski A.

Identyfikatory

DOI

10.4064/ba62-2-7

• Języki publikacji: EN

Abstrakty

EN

Let (h_k)k≥0 be the Haar system on [0,1]. We show that for any vectors ak from a separable Hilbert space H and any ε_k∈[−1,1], k=0,1,2,…, we have the sharp inequality ...[formula], where W([0,1]) is the weak-L∞ space introduced by Bennett, DeVore and Sharpley. The above estimate is generalized to the sharp weak-type bound ∥Y∥_W(Ω)≤2∥X∥_L∞(Ω), where X and Y stand for H-valued martingales such that Y is differentially subordinate to X. An application to harmonic functions on Euclidean domains is presented.

Słowa kluczowe

EN

Haar system; harmonic function; martingale; differential subordination; best constant

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2014
• Tom: Vol. 62, no 2
• Strony: 187--196
• Opis fizyczny: Bibliogr. 12 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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