Morrey estimates for parabolic nondivergence operators of Hörmander type

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1. [1] M. Bramanti - L. Brandolini, $L^p$ -estimates for nonvariational hypoelliptic operators with $VMO$ coefficients, Trans. Amer. Math. Soc., 352 (2) (2000), pp. 781--822. Zbl0935.35037MR1608289
2. [2] M. Bramanti - L. Brandolini, Schauder estimates for parabolic nondivergence operators of Hörmande type, J. Differential Equations, 234 (1) (2007), pp. 177--245. Zbl1113.35033MR2298970
3. [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. Zbl1072.35058MR1962808
4. [4] M. Bramanti - C. Cerutti, Commutators of singular integrals in homogeneous spaces, Boll. Unione Mat. Italiana, 10-B (7) (1996), pp. 843--883. Zbl0913.42013MR1430157
5. [5] M. Bramanti - C. Cerutti, $W_p^{1,2}$-solvability for the Cauchy-Dirichlet problem for parabolic equations with $VMO$ coefficients, Comm. Partial Differential Equations, 18 (9-10) (1993), pp. 1735--1763. Zbl0816.35045MR1239929
6. [6] M. Bramanti, Commutators of integral operators with positive kernels, Le Mat., XLIX, 49 (1994), pp. 149--168. Zbl0840.42009MR1386370
7. [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. Zbl0368.46037MR467176
8. [8] A. P. Calderón - A. Zygmund, Singular integral operators and differential equations, Amer. J. Math., 79 (1957), pp. 901--921. Zbl0081.33502MR100768
9. [9] Y. Z. Chen - L. C. Wu, Elliptic equation of second order and elliptic system, Science Press, Beijing, 1991. 
10. [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. Zbl0772.35017MR1191890
11. [11] F. Chiarenza - M. Frasca - P. Longo, $W^{2,p}$-solvability of the Dirichlet problem for nondivergence form elliptic equations with $VMO$ coefficients, Trans. Amer. Math. Soc., 336 (1993), pp. 841--853. Zbl0818.35023MR1088476
12. [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). Zbl0224.43006MR499948
13. [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. Zbl0942.35059MR1707751
14. [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. Zbl0822.35036MR1213138
15. [15] G. B. Folland, Subelliptic estimates and function spaces on nilpotent Lie groups, Ark. Mat., 13 (2) (1975), pp. 161--207. Zbl0312.35026MR494315
16. [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. Zbl0916.43006MR1704904
17. [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. Zbl0503.35071MR730094
18. [18] G. B. Folland - E. M. Stein, Estimates for the ${\overline{\partial }}_b$ complex and analysis on the Heisenberg group, Comm. Pure Appl. Math., 27 (4) (1974), pp. 429--522. Zbl0293.35012MR367477
19. [19] D. Gilbarg - N. S. Trudinger, Elliptic partial differential equations of second order, 2nd ed. Springer-Verlag, Berlin, 1983. Zbl0361.35003MR737190
20. [20] L. Hörmander, Hypoelliptic second order differential equations, Acta Mathematica, 119 (1967), pp. 147--171. Zbl0156.10701MR222474
21. [21] G. M. Lieberman, A mostly elementary proof of Morrey space estimates for elliptic and parabolic equations with $VMO$ coefficients, J. Funct. Anal., 201 (2) (2003), pp. 457--479. Zbl1107.35030MR1986696
22. [22] R. A. Macias - C. Segovia, Lipschitz functions on spaces of homogeneous type, Adv. Math., 33 (3) (1979), pp. 257--270. Zbl0431.46018MR546295
23. [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. Zbl0578.32044MR793239
24. [24] L. P. Rothschild - E. M. Stein, Hypoelliptic differential operators and nilpotent groups, Acta Math., 137 (1976), pp. 247--320. Zbl0346.35030MR436223
25. [25] A. Sanchez-Calle, Fundamental solutions and geometry of sum of squares of vector fields, Invent. Math., 78 (1) (1984), pp. 143--160. Zbl0582.58004MR762360