Sharp-edged square functions

Wilson, Michael

doi:10.1090/proc/14174

Sharp-edged square functions
HTML articles powered by AMS MathViewer

by Michael Wilson PDF

Proc. Amer. Math. Soc. 147 (2019), 2405-2412 Request permission

Abstract:

We prove $L^2\to L^2$ boundedness for a type of intrinsic square function in which the constituent kernels (“ wavelets”) are not assumed to have pointwise smoothness or carefully placed discontinuities. Aside from the usual assumptions of cancellation and bounded supports, we ask only that our functions be of uniformly bounded variation on lines parallel to the coordinate axes.

References

Tom M. Apostol, Mathematical analysis, 2nd ed., Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1974. MR 0344384
S.-Y. A. Chang, J. M. Wilson, and T. H. Wolff, Some weighted norm inequalities concerning the Schrödinger operators, Comment. Math. Helv. 60 (1985), no. 2, 217–246. MR 800004, DOI 10.1007/BF02567411
John B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol. 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 628971
J. Michael Wilson, Weighted norm inequalities for the continuous square function, Trans. Amer. Math. Soc. 314 (1989), no. 2, 661–692. MR 972707, DOI 10.1090/S0002-9947-1989-0972707-9
Michael Wilson, The intrinsic square function, Rev. Mat. Iberoam. 23 (2007), no. 3, 771–791. MR 2414491, DOI 10.4171/RMI/512
Michael Wilson, Weighted Littlewood-Paley theory and exponential-square integrability, Lecture Notes in Mathematics, vol. 1924, Springer, Berlin, 2008. MR 2359017
Michael Wilson, Bounded variation, convexity, and almost-orthogonality, Harmonic analysis, partial differential equations and applications, Appl. Numer. Harmon. Anal., Birkhäuser/Springer, Cham, 2017, pp. 275–301. MR 3642747