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## entrOn One Weighted Inequalities for Convolution Type OperatorOn One Weighted Inequalities for Convolution Type Operator

#### R. A. B [1] , - - [2]

In this paper we prove the boundedness of certain convolution operatorin a weighted Lebesgue space with kernel satisfying the generalizedH¨ ormander’s condition. The sufficient conditions for the pair of generalweights ensuring the validity of two-weight inequalities of a strong typeand of a weak type for convolution operator with kernel satisfying thegeneralized H¨ormander’s condition are found.
Weighted Lebesgue space, Singular integral, Kernel, Generalized H¨ormander’s condition, Boundedness.
• Bandaliev, R. A. Two-weight inequalities for convolution operators in Lebesgue spaces, Mat.Zametki, 80 (1), 3–10, 2006 (in Russian). English translation: in Math. Notes 80 (1), 3–10, 2006.
• Bandaliev, R. A. and Omarova, K. K. Two-weight norm inequalities for certain singular integrals, Taiwanese Jour. of Math., N2, 713–732, 2012.
• Calder on, A. P. and Zygmund, A. On the existence of certain singular integrals, Acta Math., 88, 85–139, 1952.
• Calder on, A. P. and Zygmund, A. On singular integrals, American Math.J., 78 (2), 289–309, 19 Davis, K. and Chang, Y. Lectures on Bochner-Riesz means, London Math. Soc., Lecture Notes ser. 114, Cambridge Univ. Press., 1987.
• Garsia-Cuerva, J. and Rubio de Francia, J. L. Weighted norm inequalities and related topics, North-Holland Math.Studies, 1985.
• Grubb, D. J. and Moore, C. N. A variant of H¨ ormander’s condition for singular integrals, Colloq. Math., 73 (2), 165–172, 1997.
• Guliyev, V. S. Two-weight inequalities for singular integrals satisfying a variant of H¨ ormander condition, Journal of Function Spaces and Appl., 7 (1), 43–54, 2009.
• H¨ ormander, L. Estimates for translation invariant operators in L p spaces, Acta Math., 104, 93–140, 1960.
• Kabaila, V. P. On the embedding L p (µ) into L q (ν). (in Russian) Litovsky Mat.Sb., 21, 143–148, 1981.
• Kokilashvili, V. and Meskhi, A. Two-weight inequalities for singular integrals defined on homogeneous groups, Proc. A.Razmadze Math.Inst., 112, 57–90, 1997.
• Maz’ya, V. G. Sobolev spaces, Springer-Verlag, Berlin, 1985.
• Stein, E. M. Note on singular integral, Proc. Amer. Math. Soc., 8(2), 250–254, 1957.
Primary Language tr Mathematics Author: R. A. B Author: - - Publication Date : March 1, 2013
 Bibtex @ { hujms101273, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2013}, volume = {42}, pages = {199 - 210}, doi = {}, title = {On One Weighted Inequalities for Convolution Type Operator}, key = {cite}, author = {B, R. A. and -, -} } APA B, R , -, - . (2013). On One Weighted Inequalities for Convolution Type Operator. Hacettepe Journal of Mathematics and Statistics , 42 (3) , 199-210 . Retrieved from https://dergipark.org.tr/en/pub/hujms/issue/7748/101273 MLA B, R , -, - . "On One Weighted Inequalities for Convolution Type Operator". Hacettepe Journal of Mathematics and Statistics 42 (2013 ): 199-210 Chicago B, R , -, - . "On One Weighted Inequalities for Convolution Type Operator". Hacettepe Journal of Mathematics and Statistics 42 (2013 ): 199-210 RIS TY - JOUR T1 - On One Weighted Inequalities for Convolution Type Operator AU - R. A. B , - - Y1 - 2013 PY - 2013 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 199 EP - 210 VL - 42 IS - 3 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2019 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics On One Weighted Inequalities for Convolution Type Operator %A R. A. B , - - %T On One Weighted Inequalities for Convolution Type Operator %D 2013 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 42 %N 3 %R %U ISNAD B, R. A. , -, - . "On One Weighted Inequalities for Convolution Type Operator". Hacettepe Journal of Mathematics and Statistics 42 / 3 (March 2013): 199-210 . AMA B R , - - . On One Weighted Inequalities for Convolution Type Operator. Hacettepe Journal of Mathematics and Statistics. 2013; 42(3): 199-210. Vancouver B R , - - . On One Weighted Inequalities for Convolution Type Operator. Hacettepe Journal of Mathematics and Statistics. 2013; 42(3): 210-199.