Title:
|
Weighted norm inequalities for singular integral operators satisfying a variant of Hörmander's condition (English) |
Author:
|
Trujillo-González, R. |
Language:
|
English |
Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
ISSN:
|
0010-2628 (print) |
ISSN:
|
1213-7243 (online) |
Volume:
|
44 |
Issue:
|
1 |
Year:
|
2003 |
Pages:
|
137-152 |
. |
Category:
|
math |
. |
Summary:
|
In this paper we establish weighted norm inequalities for singular integral operators with kernel satisfying a variant of the classical Hörmander's condition. (English) |
Keyword:
|
singular integral operators |
Keyword:
|
maximal operators |
Keyword:
|
$A_p$ weights |
MSC:
|
42B20 |
MSC:
|
42B25 |
idZBL:
|
Zbl 1127.42307 |
idMR:
|
MR2045851 |
. |
Date available:
|
2009-01-08T19:28:06Z |
Last updated:
|
2012-04-30 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119373 |
. |
Reference:
|
[1] Bagby R.J., Kurtz D.S.: Covering lemmas and the sharp function.Proc. Amer. Math. Soc. 93 (2) (1985), 291-296. Zbl 0531.42006, MR 0770539 |
Reference:
|
[2] Burkholder D.L., Gundy R.F.: Extrapolation and interpolation of quasi-linear operators on martingales.Acta Math. 124 (1970), 249-304. Zbl 0223.60021, MR 0440695 |
Reference:
|
[3] Calderón A., Zygmund A.: On the existence of certain singular integrals.Acta Math. 88 (1952), 85-139. MR 0052553 |
Reference:
|
[4] Coifman R., Fefferman C.: Weighted norm inequalities for maximal functions and singular integrals.Studia Math. 51 (1974), 241-250. Zbl 0291.44007, MR 0358205 |
Reference:
|
[5] García-Cuerva J., Rubio de Francia J.L.: Weighted Norm Inequalities and Related Topics.North-Holland Mathematics Studies 116, North-Holland, Amsterdam, 1985. MR 0848147 |
Reference:
|
[6] Grubb D.J., Moore C.N.: A variant of Hörmander condition for singular integrals.Colloq. Math. 73 (2) (1997), 165-172. MR 1446111 |
Reference:
|
[7] Hörmander L.: Estimates for translation invariant operators in $L^p$ spaces.Acta Math. 104 (1960), 93-140. MR 0121655 |
Reference:
|
[8] Journé J.L.: Calderón-Zygmund Operators, Pseudo-Differential Operator, and the Cauchy Integral of Calderón.Lecture Notes in Math., Vol. 994, Springer-Verlag, New York, 1983. MR 0706075 |
Reference:
|
[9] Mason J.C.: Near-Best $L_1$ approximation on circular and elliptical contours.J. Approx. Theory 24 (1978), 330-343. MR 0523982 |
Reference:
|
[10] Rubio de Francia J.L., Ruíz F., Torrea J.L.: Calderón-Zygmund theory for operator-valued kernels.Adv. Math. 62 (1986), 7-48. MR 0859252 |
Reference:
|
[11] Torchinsky A.: Real-Variable Methods in Harmonic Analysis.Academic Press, New York, 1987. Zbl 1097.42002, MR 0869816 |
Reference:
|
[12] Watson D.K.: Weighted estimates for singular integrals via Fourier transform estimates.Duke Math. J. 60 (2) (1990), 389-399. Zbl 0711.42025, MR 1047758 |
. |