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## 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

#### Ferit GÜRBÜZ [1]

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.
parabolic multilinear commutators, rough kernel, parabolic generalized local Morrey space, parabolic local Campanato space
• [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.
Birincil Dil en Matematik Matematik Orcid: 0000-0003-3049-688XYazar: Ferit GÜRBÜZ (Sorumlu Yazar)Kurum: HAKKARI UNIVERSITYÜlke: Turkey Yayımlanma Tarihi : 2 Nisan 2020
 Bibtex @araştırma makalesi { hujms568393, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe Üniversitesi}, year = {2020}, volume = {49}, pages = {617 - 637}, doi = {10.15672/hujms.568393}, title = {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}, key = {cite}, author = {GÜRBÜZ, Ferit} } 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 . DOI: 10.15672/hujms.568393 MLA 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 49 (2020 ): 617-637 Chicago 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 49 (2020 ): 617-637 RIS TY - JOUR T1 - 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 AU - Ferit GÜRBÜZ Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.568393 DO - 10.15672/hujms.568393 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 617 EP - 637 VL - 49 IS - 2 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.568393 UR - https://doi.org/10.15672/hujms.568393 Y2 - 2019 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics 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 %A Ferit GÜRBÜZ %T 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 %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 2 %R doi: 10.15672/hujms.568393 %U 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 (Nisan 2020): 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. 2020; 49(2): 617-637. 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): 637-617.

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