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Year 2020, Volume: 49 Issue: 2, 617 - 637, 02.04.2020
https://doi.org/10.15672/hujms.568393

Abstract

References

  • [1] D.R. Adams, Morrey spaces, Lecture Notes in Applied and Numerical Harmonic Analysis, Birkhäuser/Springer, Cham, 2015.
  • [2] A.P. Calderón and A. Torchinsky, Parabolic maximal functions associated with a distribution, Adv. Math. 16, 1-64, 1975.
  • [3] R.R. Coifman and G. Weiss, Analyse harmonique non-commutative sur certains espaces homogènes, Étude de certaines intégrales singuliàres, Lecture Notes in Mathematics, 242, Berlin-New York: Springer-Verlag, 1971, (in French).
  • [4] Y. Ding, Weak type bounds for a class of rough operators with power weights, Proc. Amer. Math. Soc. 125, 2939-2942, 1997.
  • [5] E. Fabes and N. Riviére, Singular integrals with mixed homogeneity, Stud. Math. 27, 19-38, 1966.
  • [6] G.B. Folland and E.M. Stein, Hardy Spaces on homogeneous groups, Math. Notes 28, Princeton Univ. Press, Princeton, 1982.
  • [7] F. Gürbüz, Parabolic sublinear operators with rough kernel generated by parabolic Calderón-Zygmund operators and parabolic local Campanato space estimates for their commutators on the parabolic generalized local Morrey spaces, Open Math. 14 (1), 300-323, 2016.
  • [8] F. Gürbüz Parabolic generalized local Morrey space estimates of rough parabolic sublinear operators and commutators, Adv. Math. (China) 46 (5), 765-792, 2017.
  • [9] F. Gürbüz, Some estimates for generalized commutators of rough fractional maximal and integral operators on generalized weighted Morrey spaces, Canad. Math. Bull. 60 (1), 131-145, 2017.
  • [10] C.B. Morrey, On the solutions of quasi-linear elliptic partial differential equations, Trans. Amer. Math. Soc. 43, 126-166, 1938.
  • [11] F. Soria and G. Weiss, A remark on singular integrals and power weights, Indiana Univ. Math. J. 43, 187-204, 1994.
  • [12] E.M. Stein, Note on singular integrals, Proc. Amer. Soc. Math. 8, 250-254, 1957.
  • [13] R.L. Wheeden and A. Zygmund, Measure and Integral: An Introduction to Real Analysis, vol. 43 of Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 1977.
  • [14] Q.Y. Xue, Y. Ding and K. Yabuta, Parabolic Littlewood-Paley g-function with rough kernel, Acta Math. Sin. (Engl. Ser.) 24 (12), 2049-2060, 2008.

A note for some parabolic multilinear commutators generated by a class of parabolic maximal and linear operators with rough kernel on the parabolic generalized local Morrey spaces

Year 2020, Volume: 49 Issue: 2, 617 - 637, 02.04.2020
https://doi.org/10.15672/hujms.568393

Abstract

In this paper, we give the boundedness of some parabolic multilinear commutators generated by a class of parabolic maximal and linear operators with rough kernel and parabolic local Campanato functions on the parabolic generalized local Morrey spaces, respectively. Indeed, the results in this paper are extensions of some known results.

References

  • [1] D.R. Adams, Morrey spaces, Lecture Notes in Applied and Numerical Harmonic Analysis, Birkhäuser/Springer, Cham, 2015.
  • [2] A.P. Calderón and A. Torchinsky, Parabolic maximal functions associated with a distribution, Adv. Math. 16, 1-64, 1975.
  • [3] R.R. Coifman and G. Weiss, Analyse harmonique non-commutative sur certains espaces homogènes, Étude de certaines intégrales singuliàres, Lecture Notes in Mathematics, 242, Berlin-New York: Springer-Verlag, 1971, (in French).
  • [4] Y. Ding, Weak type bounds for a class of rough operators with power weights, Proc. Amer. Math. Soc. 125, 2939-2942, 1997.
  • [5] E. Fabes and N. Riviére, Singular integrals with mixed homogeneity, Stud. Math. 27, 19-38, 1966.
  • [6] G.B. Folland and E.M. Stein, Hardy Spaces on homogeneous groups, Math. Notes 28, Princeton Univ. Press, Princeton, 1982.
  • [7] F. Gürbüz, Parabolic sublinear operators with rough kernel generated by parabolic Calderón-Zygmund operators and parabolic local Campanato space estimates for their commutators on the parabolic generalized local Morrey spaces, Open Math. 14 (1), 300-323, 2016.
  • [8] F. Gürbüz Parabolic generalized local Morrey space estimates of rough parabolic sublinear operators and commutators, Adv. Math. (China) 46 (5), 765-792, 2017.
  • [9] F. Gürbüz, Some estimates for generalized commutators of rough fractional maximal and integral operators on generalized weighted Morrey spaces, Canad. Math. Bull. 60 (1), 131-145, 2017.
  • [10] C.B. Morrey, On the solutions of quasi-linear elliptic partial differential equations, Trans. Amer. Math. Soc. 43, 126-166, 1938.
  • [11] F. Soria and G. Weiss, A remark on singular integrals and power weights, Indiana Univ. Math. J. 43, 187-204, 1994.
  • [12] E.M. Stein, Note on singular integrals, Proc. Amer. Soc. Math. 8, 250-254, 1957.
  • [13] R.L. Wheeden and A. Zygmund, Measure and Integral: An Introduction to Real Analysis, vol. 43 of Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 1977.
  • [14] Q.Y. Xue, Y. Ding and K. Yabuta, Parabolic Littlewood-Paley g-function with rough kernel, Acta Math. Sin. (Engl. Ser.) 24 (12), 2049-2060, 2008.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Ferit Gürbüz 0000-0003-3049-688X

Publication Date April 2, 2020
Published in Issue Year 2020 Volume: 49 Issue: 2

Cite

APA Gürbüz, F. (2020). A note for some parabolic multilinear commutators generated by a class of parabolic maximal and linear operators with rough kernel on the parabolic generalized local Morrey spaces. Hacettepe Journal of Mathematics and Statistics, 49(2), 617-637. https://doi.org/10.15672/hujms.568393
AMA Gürbüz F. A note for some parabolic multilinear commutators generated by a class of parabolic maximal and linear operators with rough kernel on the parabolic generalized local Morrey spaces. Hacettepe Journal of Mathematics and Statistics. April 2020;49(2):617-637. doi:10.15672/hujms.568393
Chicago Gürbüz, Ferit. “A Note for Some Parabolic Multilinear Commutators Generated by a Class of Parabolic Maximal and Linear Operators With Rough Kernel on the Parabolic Generalized Local Morrey Spaces”. Hacettepe Journal of Mathematics and Statistics 49, no. 2 (April 2020): 617-37. https://doi.org/10.15672/hujms.568393.
EndNote Gürbüz F (April 1, 2020) A note for some parabolic multilinear commutators generated by a class of parabolic maximal and linear operators with rough kernel on the parabolic generalized local Morrey spaces. Hacettepe Journal of Mathematics and Statistics 49 2 617–637.
IEEE F. Gürbüz, “A note for some parabolic multilinear commutators generated by a class of parabolic maximal and linear operators with rough kernel on the parabolic generalized local Morrey spaces”, Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 2, pp. 617–637, 2020, doi: 10.15672/hujms.568393.
ISNAD Gürbüz, Ferit. “A Note for Some Parabolic Multilinear Commutators Generated by a Class of Parabolic Maximal and Linear Operators With Rough Kernel on the Parabolic Generalized Local Morrey Spaces”. Hacettepe Journal of Mathematics and Statistics 49/2 (April 2020), 617-637. https://doi.org/10.15672/hujms.568393.
JAMA Gürbüz F. A note for some parabolic multilinear commutators generated by a class of parabolic maximal and linear operators with rough kernel on the parabolic generalized local Morrey spaces. Hacettepe Journal of Mathematics and Statistics. 2020;49:617–637.
MLA Gürbüz, Ferit. “A Note for Some Parabolic Multilinear Commutators Generated by a Class of Parabolic Maximal and Linear Operators With Rough Kernel on the Parabolic Generalized Local Morrey Spaces”. Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 2, 2020, pp. 617-3, doi:10.15672/hujms.568393.
Vancouver Gürbüz F. A note for some parabolic multilinear commutators generated by a class of parabolic maximal and linear operators with rough kernel on the parabolic generalized local Morrey spaces. Hacettepe Journal of Mathematics and Statistics. 2020;49(2):617-3.