Lp estimates for uniformly hypoelliptic operators with discontinuous coefficients on homogeneous groups

Rendiconti del Seminario Matematico

Volumn 58, Issue 4, 2000, Pages 389-434

  Bramanti, M ^a   Brandolini, L ^b  

^a POLITECNICO DI MILANO   (Italy)

^b UNIVERSITY OF BERGAMO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 27344431988     PISSN: 03731243     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (31)

1. AGMON S., DOUGLIS A. AND NIRENBERG L., Estimates near the boundary for solutions of elliptic partial differential eqautions satisfying general boundary conditions, Comm. Pure Appl. Math., 12(1959), 623-727 and 17(1964), 35-92.
2. p-estimates for nonvariational hypoelliptic operators with VMO coefficients, Trans. of the Amer. Math. Soc., 352(2000), 781-822.
3. 1, 2-solvability for the Cauchy-Dirichlet problem for parabolic equations with VMO coefficients, Comm. in Part. Diff. Eq., 18 9-10(1993), 1735-1763.
4. BRAMANTI M. AND CERUTTI C., Commutators of singular integrals in homogeneous spaces, Boll. Unione Mat. Italiana, 710B (1996), 843-883.
5. p-estimates for some ultraparabolic operators with discontinuous coefficients, J. Math. Anal. and Appl., 200(1996), 332-354.
6. 2, p-estimatesfor nondivergence elliptic equations with discontinuous coefficients, Ricerche di Mat. XL (1991), 149-168.
7. 2, p-solvability of the Dirichlet problem for non divergence elliptic equations with VMO coefficients, Trans. Am. Math. Soc. 336 1(1993), 841-853.
8. COIFMAN R., ROCHBERG R. AND WEISS G., Factorization theorems for Hardy spaces in several variables, Annals Math. 103(1976), 611-635.
9. COIFMAN R. AND WEISS G., Analyse Harmonique Non-Commutative sur Certains Espaces Homogenes, Lecture Notes in Mathematics 242, Springer-Verlag, Berlin-Heidelberg-New York 1971.
10. CALDERON A. P. AND ZYGMUND A., Singular integral operators and differential equations, Am. Journ. of Math. 79(1957), 901-921.
11. FOLLAND F. B., Subelliptic estimates and function spaces on nilpotent Lie groups, Arkiv for Math. 13(1975), 161-207.
12. FABES E. B. AND RIVIERE N., Singular integrals with mixed homogeneity, Studia Mathematica 27(1966), 19-38.
13. FOLLAND F. B. AND STEIN E. M., Estimates for the 9b complex and analysis on the Heisenberg group, Comm. Pure and Appl. Math. XXVII (1974), 429-522.
14. GILBARG D. AND TRUDINGER N. S., Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin Heidelberg New York Tokio 1983 (2nd ed.).
15. GATTO A. E. AND VÁGI S., Fractional Integrals on Spaces of Homogeneous Type. Analysis and Partial Differential Equations, ed. by Cora Sadosky, Lecture Notes in Pure and Applied Math. 122(1990), 171-216.
16. HÖRMANDER L., Hypoelliptic second order differential equations, Acta Mathematica, 119(1967), 147-171.
17. ILYIN V. A. AND POZNYAK E. G., Linear Algebra, MIR Publisher, Moscow 1986.
18. JOHN F. AND NIRENBERG N., On functions of bounded mean oscillation, Comm. Pure Appl. Math., 14(1961), 175-188.
19. JERISON D. AND SANCHEZ-CALLE A., Estimates for the heat kernel for a sum of squares of vector fields, Indiana Univ. Math. Jour. 35 4(1986), 835-854.
20. KNAPP A. W. AND STEIN E. M., Intertwining operators for semi-simple groups, Ann. of Math. 93(1971), 489-578.
21. KOHN J. J., Pseudo-differential operators and hypoellipticity, Proc. Symp. Pure Math. Amer. Math. Soc. 23(1973), 61-69.
22. LANCONELLI E. AND LASCIALFARI F., A boundary value problem for a class of quasilinear operators of Fokker-Planck type, Ann. Univ. Ferrara Sez. VII 40(1995), 65-84.
23. LANCONELLI E. AND POLIDORO S., On a class of hypoelliptic evolution operators, Rend. Sem. Mat. Polit. Torino 51 4(1993), 137-171.
24. MANFREDINI M., The Dirichlet problem for a class of ultraparabolic equations, Advances in Differential Equations 2 5(1997), 831-866.
25. MANFREDINI M. AND POLIDORO S., Interior regularity for weak solutions of ultraparabolic equations in divergence form with discontinuous coefficients, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. 8 1(1998), no. 3, 651-675.
26. A. NAGEL A., STEIN E. M. AND WAINGER S., Balls and metrics defined by vector fields I: Basic properties, Acta Mathematica 155(1985), 130-147.
27. MANFREDINI M. AND POLIDORO S., A global lower bound for the fundamental solution of Kolmogorov-Fokker-Planck equations, Arch. Rational Mech. Anal. 137 4(1997), 321-340.
28. ROTHSCHILD L. P. AND STEIN E. M., Hypoelliptic differential operators and nilpotent groups, Acta Math. 137(1976), 247-320.
29. SANCHEZ-CALLE A., Fundamental solutions and geometry of sum of squares of vector fields Inv. Math. 78(1984), 143-160.
30. SARASON D., Functions of vanishing mean oscillations Trans. of Am. Math. Soc. 207(1974), 391-405.
31. STEIN E. M., Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integrals, Princeton Univ. Press. Princeton, New Jersey 1993.