Geodesic
Adams-Spanne type estimates for parabolic sublinear operators and their commutators with rough kernels on parabolic generalized Morrey spaces
Gürbüz, Ferit1
1 Department of Mathematics Education, Faculty of Education, Hakkary Uinversity, Hakkari, Turkey
Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 6, p. 798-811.

Voir la notice de l'article provenant de la source International Scientific Research Publications

The aim of this paper is to give Adams-Spanne type estimates for parabolic sublinear operators and their commutators by with rough kernels generated by parabolic fractional integral operators under generic size conditions which are satisfied by most of the operators in harmonic analysis. Their endpoint estimates are also disposed.
DOI : 10.22436/jnsa.011.06.07
Classification : 42B20, 42B25, 42B35
Keywords: Parabolic sublinear operator, parabolic fractional integral operator, parabolic fractional maximal operator, rough kernel, parabolic generalized Morrey space, parabolic BMO space, commutator

Gürbüz, Ferit 1

1 Department of Mathematics Education, Faculty of Education, Hakkary Uinversity, Hakkari, Turkey 
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Gürbüz, Ferit. Adams-Spanne type estimates for parabolic sublinear operators and their commutators with rough kernels on parabolic generalized Morrey spaces. Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 6, p. 798-811. doi : 10.22436/jnsa.011.06.07. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.011.06.07/

[1] D. R. Adams A note on Riesz potentials, Duke Math. J., Volume 42 (1975), pp. 765-778 | DOI | Zbl

[2] Calderón, A.-P. Commutators of singular integral operators, Proc. Nat. Acad. Sci. U.S.A., Volume 53 (1965), pp. 1092-1099

[3] Calderón, A.-P.; A. Torchinsky Parabolic maximal functions associated with a distribution, Advances in Math., Volume 16 (1975), pp. 1-64 | DOI

[4] Coifman, R. R.; G.Weiss Analyse harmonique non-commutative sur certains espaces homogànes, Springer-Verlag, Berlin- New York, 1971 | DOI

[5] Fabes, E. B.; N. M. Rivière Singular integrals with mixed homogeneity, Studia Math., Volume 27 (1966), pp. 19-38 | DOI

[6] Folland, G. B.; Stein, E. M. Hardy Spaces on homogeneous groups, Princeton University Press, Princeton, New Jersey, 1982

[7] Guliyev, V. S.; A. S. Balakishiyev Parabolic fractional maximal and integral operators with rough kernels in parabolic generalized Morrey spaces, J. Math. Inequal., Volume 9 (2015), pp. 257-276 | Zbl

[8] Gürbüz, F. Parabolic generalized local Morrey space estimates of rough parabolic sublinear operators and commutators, Adv. Math. (China), Volume 46 (2017), pp. 765-792

[9] F. Gürbüz Sublinear operators with rough kernel generated by Calderón-Zygmund operators and their commutators on generalized Morrey spaces, Math. Notes, Volume 101 (2017), pp. 429-442

[10] Gürbüz, F. Weighted anisotropic Morrey Spaces estimates for anisotropic maximal operators, J. Adv. Appl. Math. (JAAM), Volume 2 (2017), pp. 143-150

[11] John, F.; Nirenberg, L. On functions of bounded mean oscillation, Comm. Pure Appl. Math., Volume 14 (1961), pp. 415-426 | DOI

[12] Li, X.; D. Yang Boundedness of some sublinear operators on Herz spaces, Illinois J. Math., Volume 40 (1996), pp. 484-501 | Zbl

[13] Morrey, C. B. On the solutions of quasi-linear elliptic partial differential equations, Trans. Amer. Math. Soc., Volume 43 (1938), pp. 126-166 | DOI

[14] Peetre, J. On the theory of \(L_{p,\lambda}\), J. Funct. Anal., Volume 4 (1969), pp. 71-87 | DOI

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