Martingale transforms with unbounded multipliers

Martingale transforms with unbounded multipliers
HTML articles powered by AMS MathViewer

by J.-A. Chao and R.-L. Long PDF

Proc. Amer. Math. Soc. 114 (1992), 831-838 Request permission

The boundedness of martingale transforms with the "multiplier" sequence in various classes is studied.

References

Rodrigo Bañuelos and Andrew G. Bennett, Paraproducts and commutators of martingale transforms, Proc. Amer. Math. Soc. 103 (1988), no. 4, 1226–1234. MR 955015, DOI 10.1090/S0002-9939-1988-0955015-6
Klaus Bichteler, Stochastic integration and $L^{p}$-theory of semimartingales, Ann. Probab. 9 (1981), no. 1, 49–89. MR 606798
D. L. Burkholder, Martingale transforms, Ann. Math. Statist. 37 (1966), 1494–1504. MR 208647, DOI 10.1214/aoms/1177699141
D. L. Burkholder, Distribution function inequalities for martingales, Ann. Probability 1 (1973), 19–42. MR 365692, DOI 10.1214/aop/1176997023
D. L. Burkholder and R. F. Gundy, Extrapolation and interpolation of quasi-linear operators on martingales, Acta Math. 124 (1970), 249–304. MR 440695, DOI 10.1007/BF02394573
Ronald R. Coifman and Yves Meyer, Au delà des opérateurs pseudo-différentiels, Astérisque, vol. 57, Société Mathématique de France, Paris, 1978 (French). With an English summary. MR 518170

A simple proof of a theorem of G. David and J. L. Joruné on singular integral operators

Burgess Davis, On the integrability of the martingale square function, Israel J. Math. 8 (1970), 187–190. MR 268966, DOI 10.1007/BF02771313
Richard F. Gundy, A decomposition for $L^{1}$-bounded martingales, Ann. Math. Statist. 39 (1968), 134–138. MR 221573, DOI 10.1214/aoms/1177698510

-spaces of martingales

28

D. Lépingle, Sur certains commutateurs de la théorie des martingales, Séminaire de Probabilités, XII (Univ. Strasbourg, Strasbourg, 1976/1977) Lecture Notes in Math., vol. 649, Springer, Berlin, 1978, pp. 138–147 (French). MR 520003