Morrey estimates for parabolic nondivergence operators of Hörmander type

Tang, Sufang; Niu, Pengcheng

Tang, Sufang ; Niu, Pengcheng

Rendiconti del Seminario Matematico della Università di Padova, Tome 123 (2010), pp. 91-130.

EuDML MR Zbl

@article{RSMUP_2010__123__91_0,
     author = {Tang, Sufang and Niu, Pengcheng},
     title = {Morrey estimates for parabolic nondivergence operators of {H\"ormander} type},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {91--130},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {123},
     year = {2010},
     mrnumber = {2683293},
     zbl = {1230.35142},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_2010__123__91_0/}
}

TY  - JOUR
AU  - Tang, Sufang
AU  - Niu, Pengcheng
TI  - Morrey estimates for parabolic nondivergence operators of Hörmander type
JO  - Rendiconti del Seminario Matematico della Università di Padova
PY  - 2010
SP  - 91
EP  - 130
VL  - 123
PB  - Seminario Matematico of the University of Padua
UR  - http://www.numdam.org/item/RSMUP_2010__123__91_0/
LA  - en
ID  - RSMUP_2010__123__91_0
ER  -

%0 Journal Article
%A Tang, Sufang
%A Niu, Pengcheng
%T Morrey estimates for parabolic nondivergence operators of Hörmander type
%J Rendiconti del Seminario Matematico della Università di Padova
%D 2010
%P 91-130
%V 123
%I Seminario Matematico of the University of Padua
%U http://www.numdam.org/item/RSMUP_2010__123__91_0/
%G en
%F RSMUP_2010__123__91_0

Tang, Sufang; Niu, Pengcheng. Morrey estimates for parabolic nondivergence operators of Hörmander type. Rendiconti del Seminario Matematico della Università di Padova, Tome 123 (2010), pp. 91-130. http://www.numdam.org/item/RSMUP_2010__123__91_0/

Bibliographie
Cité par

[1] M. Bramanti - L. Brandolini, $L^{p}$ -estimates for nonvariational hypoelliptic operators with $V M O$ coefficients, Trans. Amer. Math. Soc., 352 (2) (2000), pp. 781--822. | MR | Zbl

[2] M. Bramanti - L. Brandolini, Schauder estimates for parabolic nondivergence operators of Hörmande type, J. Differential Equations, 234 (1) (2007), pp. 177--245. | MR | Zbl

[3] M. Bramanti - L. Brandolini, $L^{p}$ -estimates for uniformly hypoelliptic operators with discontinuous coefficients on homogenous groups, Rend. Sem. Mat. Univ. Politec. Torino, 58 (4) (2000), pp. 389--433. | MR | Zbl

[4] M. Bramanti - C. Cerutti, Commutators of singular integrals in homogeneous spaces, Boll. Unione Mat. Italiana, 10-B (7) (1996), pp. 843--883. | MR | Zbl

[5] M. Bramanti - C. Cerutti, $W_{p}^{1, 2}$ -solvability for the Cauchy-Dirichlet problem for parabolic equations with $V M O$ coefficients, Comm. Partial Differential Equations, 18 (9-10) (1993), pp. 1735--1763. | MR | Zbl

[6] M. Bramanti, Commutators of integral operators with positive kernels, Le Mat., XLIX, 49 (1994), pp. 149--168. | MR | Zbl

[7] N. Burger, Espace des functions à variation moyenne bornée sur un espace de nature homogène, C.R. Math. Acad. Sci. Paris, 286 (1978), pp. 139--142. | MR | Zbl

[8] A. P. Calderón - A. Zygmund, Singular integral operators and differential equations, Amer. J. Math., 79 (1957), pp. 901--921. | MR | Zbl

[9] Y. Z. Chen - L. C. Wu, Elliptic equation of second order and elliptic system, Science Press, Beijing, 1991.

[10] F. Chiarenza - M. Frasca - P. Longo, Interior $W^{2, p}$ -estimates for nondivergence elliptic equations with discontinuous coefficients, Ricerche Mat., 40 (1991), pp. 149--168. | MR | Zbl

[11] F. Chiarenza - M. Frasca - P. Longo, $W^{2, p}$ -solvability of the Dirichlet problem for nondivergence form elliptic equations with $V M O$ coefficients, Trans. Amer. Math. Soc., 336 (1993), pp. 841--853. | MR | Zbl

[12] R. Coifman - G. Weiss, Analyse Harmonique Non-Commutative sur Certains Espaces Homognes, in: Lecture Notes in Mathematics, Vol. 242 (Springer-Verlag, Berlin-Heidelberg-New York, 1971). | MR | Zbl

[13] G. Di Fazio - D. K. Palagachev - M. A. Ragusa, Global Morrey regularity of strong solutions to the Dirichlet problem for elliptic equations with discontinuous coefficients, J. Funct. Anal., 166 (2) (1999), pp. 179--196. | MR | Zbl

[14] G. Di Fazio - M. A. Ragusa, Interior estimates in Morrey spaces for strong solutions to nondivergence form elliptic equations with discontinuous coefficients, J. Funct. Anal., 112 (2) (1993), pp. 241--256. | MR | Zbl

[15] G. B. Folland, Subelliptic estimates and function spaces on nilpotent Lie groups, Ark. Mat., 13 (2) (1975), pp. 161--207. | MR | Zbl

[16] D. S. Fan - S. Z. Lu - D. C. Yang, Boundedness of operators in Morrey spaces on homogenous spaces and its application, Acta. Math. Sinica (New Series), 14 (4) (1998), pp. 625--634. | MR | Zbl

[17] C. Fefferman - D. H. Phong, Subelliptic eigenvalue problems, in: Proceedings of the Conference on harmonic Analysis in honor of Antoni Zygmund, pp. 590--606, Wadsworth Math. Series, 1981. | MR | Zbl

[18] G. B. Folland - E. M. Stein, Estimates for the ${\bar{\partial}}_{b}$ complex and analysis on the Heisenberg group, Comm. Pure Appl. Math., 27 (4) (1974), pp. 429--522. | MR | Zbl

[19] D. Gilbarg - N. S. Trudinger, Elliptic partial differential equations of second order, 2nd ed. Springer-Verlag, Berlin, 1983. | MR | Zbl

[20] L. Hörmander, Hypoelliptic second order differential equations, Acta Mathematica, 119 (1967), pp. 147--171. | MR | Zbl

[21] G. M. Lieberman, A mostly elementary proof of Morrey space estimates for elliptic and parabolic equations with $V M O$ coefficients, J. Funct. Anal., 201 (2) (2003), pp. 457--479. | MR | Zbl

[22] R. A. Macias - C. Segovia, Lipschitz functions on spaces of homogeneous type, Adv. Math., 33 (3) (1979), pp. 257--270. | MR | Zbl

[23] A. Nagel - E. M. Stein - S. Wainger, Balls and metrics defined by vector fields I:Basic properties, Acta Math., 155 (1985), pp. 103--147. | MR | Zbl

[24] L. P. Rothschild - E. M. Stein, Hypoelliptic differential operators and nilpotent groups, Acta Math., 137 (1976), pp. 247--320. | MR | Zbl

[25] A. Sanchez-Calle, Fundamental solutions and geometry of sum of squares of vector fields, Invent. Math., 78 (1) (1984), pp. 143--160. | MR | Zbl