BibTex RIS Kaynak Göster

On One Weighted Inequalities for Convolution Type Operator

Yıl 2013, Cilt: 42 Sayı: 3, 199 - 210, 01.03.2013

Öz

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.

Kaynakça

  • 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.

On One Weighted Inequalities for Convolution Type Operator

Yıl 2013, Cilt: 42 Sayı: 3, 199 - 210, 01.03.2013

Öz

-

Kaynakça

  • 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.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Matematik
Yazarlar

R. A. B Bu kişi benim

- - Bu kişi benim

Yayımlanma Tarihi 1 Mart 2013
Yayımlandığı Sayı Yıl 2013 Cilt: 42 Sayı: 3

Kaynak Göster

APA B, R. A., & -, .-. (2013). On One Weighted Inequalities for Convolution Type Operator. Hacettepe Journal of Mathematics and Statistics, 42(3), 199-210.
AMA B RA, -. On One Weighted Inequalities for Convolution Type Operator. Hacettepe Journal of Mathematics and Statistics. Mart 2013;42(3):199-210.
Chicago B, R. A., ve - -. “On One Weighted Inequalities for Convolution Type Operator”. Hacettepe Journal of Mathematics and Statistics 42, sy. 3 (Mart 2013): 199-210.
EndNote B RA, - - (01 Mart 2013) On One Weighted Inequalities for Convolution Type Operator. Hacettepe Journal of Mathematics and Statistics 42 3 199–210.
IEEE R. A. B ve .-. -, “On One Weighted Inequalities for Convolution Type Operator”, Hacettepe Journal of Mathematics and Statistics, c. 42, sy. 3, ss. 199–210, 2013.
ISNAD B, R. A. - -, -. “On One Weighted Inequalities for Convolution Type Operator”. Hacettepe Journal of Mathematics and Statistics 42/3 (Mart 2013), 199-210.
JAMA B RA, - -. On One Weighted Inequalities for Convolution Type Operator. Hacettepe Journal of Mathematics and Statistics. 2013;42:199–210.
MLA B, R. A. ve - -. “On One Weighted Inequalities for Convolution Type Operator”. Hacettepe Journal of Mathematics and Statistics, c. 42, sy. 3, 2013, ss. 199-10.
Vancouver B RA, - -. On One Weighted Inequalities for Convolution Type Operator. Hacettepe Journal of Mathematics and Statistics. 2013;42(3):199-210.