Uncertainty Principle Estimates for Vector Fields

Journal of Functional Analysis

Volumn 181, Issue 1, 2001, Pages 146-188

  Pérez, Carlos ^a   Wheeden, Richard L ^b  

^a UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

^b RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038340542     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.2000.3711     Document Type: Article

References (46)

1. Adams D. R. Weighted nonlinear potential theory. Trans. Amer. Math. Soc. 297:1986;73-94.
2. Bennett C., Sharpley R. C. Interpolation of Operators. Pure Appl. Math. 129:1988;Academic Press, San Diego.
3. Bernardis A., Salinas O. Two-weight norm inequalities for the fractional maximal operator on spaces of homogeneous type. Studia Math. 108:1994;201-207.
4. Coifman R. R., Weiss G. Analyse harmonique non-commutative sur certains espaces homogènes. Lecture Notes in Math. 1971;Springer-Verlag, New York/Berlin.
5. Chang A., Wilson M., Wolff T. Some weighted norm inequalities concerning the Schödinger operator. Comment. Math. Helv. 60:1985;217-246.
6. p estimates for fractional integrals and Sobolev inequalities with applications to Schrödinger operators. Comm. Partial Differential Equations. 10:1985;1077-1116.
7. Cruz-Uribe D., Pérez C. Two weight extrapolation via the maximal operator. J. Funct. Anal. 174:2000;1-17.
8. Cruz-Uribe D., Pérez C. Two-weight, weak-type norm inequalities for singular integral operators. Math. Res. Lett. 6:1999;1-11.
9. Danielli D. A Fefferman-Phong inequality and applications to quasilinear subelliptic equations. Potential Anal. 11:1999;387-413.
10. Fefferman C., Phong D. H. Subelliptic eigenvalue estimates. Beckner W. Conference on Harmonic Analysis, Chicago. 1981;590-606 Wadsworth, Belmont.
11. Franchi B., Lanconelli E. Hölder regularity theorem for a class of linear nonuniformly elliptic operators with measurable coefficients. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4). 10:1983;523-541.
12. Franchi B., Lu G., Wheeden R. L. Representation formulas and weighted Poincaré inequalities for Hörmander vector fields. Ann. Inst. Fourier. 45:1995;577-604.
13. Franchi B., Gutiérrez C. E., Wheeden R. L. Weighted Sobolev-Poincaré inequalities for Grushin type operators. Comm. Partial Differential Equations. 19:1994;523-604.
14. Genebashvili I., Gogatishvili A., Kokilashvili V. Criteria of general weak type inequalities for integral transforms with positive kernels. Proc. Georgian Acad. Sci. (Math.). 1:1993;11-34.
15. Greco I., Iwaniec T. New inequalities for the Jacobian. Ann. Inst. H. Poincaré 11:1994;17-35.
16. Gabidzashvili M., Kokilashvili V. Two weight weak type inequalities for fractional type integrals. Ceskoslovenska Akad. Ved. 45:1989;1-11.
17. Hörmander L. Hypoelliptic second order differential equations. Acta Math. 119:1967;147-171.
18. Hardy G., Littlewood J. E., Polya G. Inequalities. 1934;Cambridge Univ. Press, Cambridge.
19. Jerison D. The Poincaré inequality for vector fields satisfying Hörmander's condition. Duke Math. J. 53:1986;503-523.
20. Jawerth B., Pérez C., Welland G. The positive cone in Triebel-Lizorkin spaces and the relation among potential and maximal operators. Milman M. Contemporary Mathematics. 1989;Amer. Math. Soc. Providence.
21. MacManus P., Pérez C. Generalized Poincaré inequalities: Sharp Self-Improving Properties. Internat. Math. Res. Notices. 2:1998;101-116.
22. Macias R., Segovia C. Lipschitz functions on spaces of homogeneous type. Adv. Math. 33:1979;257-270.
23. Muckenhoupt B., Wheeden R. L. Weighted norm inequalities for fractional integrals. Trans. Amer. Math. Soc. 192:1974;261-275.
24. Nagel A., Stein E. M., Wainger S. Balls and metrics defined by vector fields. I. Basic properties. Acta Math. 155:1985;103-147.
25. p weights. Proc. Amer. Math. Soc. 87:1983;272-276.
26. p, q spaces. J. Anal. Math. 21:1968;1-276.
27. Pérez C. Two weighted norm inequalities for potential and fractional maximal operators. Indiana Univ. Math. J. 43:1994;663-683.
28. p-weighted Sobolev inequalities. Ann. Inst. Fourier. 45:1995;809-824.
29. p-spaces with different weights. Proc. London Math. Soc. 71:1995;135-157.
30. Pérez C. Weighted norm inequalities for singular integral operators. J. London Math. Soc. 49:1994;296-308.
31. Pérez C. Sharp estimates for commutators of singular integrals via iterations of the Hardy-Littlewood maximal function. J. Fourier Anal. Appl. 3:1997;743-756.
32. Pérez C. Sharp weighted inequalities for the vector-valued maximal function. Trans. Amer. Math. Soc. 352:2000;3265-3288.
33. Pérez C. Endpoint estimates for commutators of singular integral operators. J. Funct. Anal. 127:1995;163-185.
34. C. Pérez, and, R. L. Wheeden, Norm estimates relating fractional integrals and maximal functions, preprint.
35. Rakotondratsimba Y. Improved Muckenhoupt-Wheeden inequality and weighted inequalities for potential operators. Publ. Mat. 39:1995;23-41.
36. Rao M., Ren Z. Theory of Orlicz Spaces. 1991;Dekker, New York.
37. Reed M., Simon B. Methods of Modern Mathematical Physics. 1975;Academic Press, San Diego.
38. Sawyer E. T. A characterization of two weight norm inequalities for fractional and Poisson integrals. Trans. Amer. Math. Soc. 308:1988;533-545.
39. Sawyer E. T., Wheeden R. L. Weighted inequalities for fractional integrals on Euclidean and homogeneous spaces. Amer. J. Math. 114:1992;813-874.
40. Sawyer E. T., Wheeden R. L., Zhao S. Weighted inequalities for operators of potential type and fractional maximal functions. Potential Anal. 5:1996;523-580.
41. Stein E. M. Note on the class L log L. Studia Math. 32:1969;305-310.
42. ∞ weights, preprint, 1997.
43. Verbitsky I. E., Wheeden R. L. Weighted norm inequalities for integral operators. Trans. Amer. Math. Soc. 350:1998;3371-3391.
44. Wheeden R. L. A characterization of some weighted norm inequalities for the fractional maximal function. Studia Math. 107:1993;251-272.
45. Wheeden R. L., Wilson J. M. Weighted norm estimates for gradients of half-space extensions. Indiana Univ. Math. J. 44:1995;917-969.
46. Wheeden R. L., Zhao S. Weak type estimates for operators of potential type. Studia Math. 119:1996;149-160.