Ping LI
,
Congbian MA
,
Youliang HOU
. THE OSCILLATION OF THE POISSON SEMIGROUP ASSOCIATED TO PARABOLIC HERMITE OPERATOR[J]. Acta mathematica scientia, Series B, 2018
, 38(4)
: 1214
-1226
.
DOI: 10.1016/S0252-9602(18)30809-9
[1] Betancor J J, Crescimbeni R, Torrea J L. The ρ-variation of the heat semigroup in the Hermitian setting:behaviour in L∞. Proc Edinburgh Math Soc (Series 2), 2011, 54:569-585
[2] Crescimbeni R, Macías R A. Menárguez T, Torrea J L, Viviani B. The ρ-variation as an operator between maximal operators and singular integrals. J Evolution Equations, 2009, 9(1):81-102
[3] Campbell J T, Jones R L, Reinhold K, Wierdl M. Oscillation and variation for singular integrals in higher dimensions. Trans Amer Math Soc, 2003, 355:2115-2137
[4] Calderón A P, Zygmund A. On the existence of certain singular integrals. Acta Math, 1952, 88:85-139
[5] Harboure E, Macías R A, Menárguez M T, Torrea J L. Oscillation and variation for the Gaussian Riesz transforms and Poisson integral. Proc Royal Soc Edinburgh, 2005, 135A:85-104
[6] Jones R L, Kaufman R, Rosenblatt J M, Wierdl M. Oscillation in ergodic theory. Ergod Theory Dynam Sys, 1998, 18:889-935
[7] Jones R L, Reinhold K. Oscillation and variation inequalities for convolution powers. Ergod Theory Dynam Sys, 2001, 21:18091829
[8] Jones R L, Rosenblatt J M, Wierdl M. Oscillation in ergodic theory:higher dimensional results. Isreal J Math, 2003, 135:1-27
[9] Li P, Torrea J L. The oscilation of the Poisson semigroup associated with parabolic Laplican operator. Submitted
[10] Li P, Stinga P R, Torrea J L. On weighted mixed-norm Sobolev estimates for some basic parabolic equations. Commun Pure Appl Anal, 2017, 16(3):855-882
[11] Ma T, Torrea J L, Xu Q. Weighted variation inequalities for differential operators and singular integrals. J Funct Anal, 2013, 265:545-561
[12] de Francia R J L, Ruiz F J, Torrea J L. Calderón-Zygmund theory for operator-valued kernels. Adv Math, 1986, 62:7-48
[13] Ruiz F J, Torrea J L. Vector-valued Calderón-Zygmund theory and Carleson measures on spaces of homogeneous nature. Studia Math, 1988, 88:221-243
[14] Stein E M. Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. Annals of Mathematics Studies, 63. Princeton, NJ:Princeton Univ Press, 1970
[15] Stinga P R, Torrea J L. Regularity theory and extension problem for fractional nonlocal parabolic equations and the master equation. SIAM J Math Anal, 2017, 49(5):3893-3924
[16] Thangavelu S. Lectures on Hermite and Laguerre Expansions. Mathematical Notes 42. Princeton, NJ:Princeton University Press, 1993
[17] Wang S. Some properties of Littlewood-Paley g-function. Sci Sinica A, 1985, 28(3):252262