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- W1602518532 abstract "AbstractWe give a class of Fourier multipliers with non-symmetric symbolsand explicit norm bounds on L p spaces by using the stochastic calculus ofLe´vy processes and Burkholder-Wang estimates for differentially subordi-nate martingales. 1 Introduction and main result For each function m : R d → Cof absolute value bounded by 1, there is a uniquelinear contraction M on L 2 (R d ) defined in terms of the Fourier transform byMfd = mf ,ˆ (1)or, in terms of bilinear forms and Plancherel theorem, byΛ(f,g) =Z R d Mf(x)g(x)dx = (2π) −d Z R d m(ξ)fb(ξ)bg(−ξ)dξ. (2) ∗ Corresponding author: Institute of Mathematics of the Polish Academy of Sciences, andInstitute of Mathematics, Wroclaw University of Technology, 50-370 Wroclaw, Poland, bog-dan@im.pwr.wroc.pl. Supported in part by grant MNiSW N N201 397137. † Mathematical Institute, University of Wroclaw, 50-384 Wroclaw, Poland, lu-woj@math.uni.wroc.pl. 0 2010 MS Classification : 42B15, 60G15, 60G46.Key words and phrases: non-symmetric Fourier multiplier, martingale transform." @default.
- W1602518532 created "2016-06-24" @default.
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- W1602518532 date "2012-06-03" @default.
- W1602518532 modified "2023-09-27" @default.
- W1602518532 title "Parabolic martingales and non-symmetric Fourier multipliers" @default.
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