BOUNDEDNESS CRITERION FOR SUBLINEAR OPERATORS AND COMMUTATORS ON GENERALIZED MIXED MORREY SPACES

Mingquan Wei

doi:10.11948/20210492

2022 Volume 12 Issue 6

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2022 > 12(6): 2349-2369

Next Article Previous Article

Mingquan Wei. BOUNDEDNESS CRITERION FOR SUBLINEAR OPERATORS AND COMMUTATORS ON GENERALIZED MIXED MORREY SPACES[J]. Journal of Applied Analysis & Computation, 2022, 12(6): 2349-2369. doi: 10.11948/20210492

Citation:

Mingquan Wei. BOUNDEDNESS CRITERION FOR SUBLINEAR OPERATORS AND COMMUTATORS ON GENERALIZED MIXED MORREY SPACES[J]. Journal of Applied Analysis & Computation, 2022, 12(6): 2349-2369. doi: 10.11948/20210492

BOUNDEDNESS CRITERION FOR SUBLINEAR OPERATORS AND COMMUTATORS ON GENERALIZED MIXED MORREY SPACES

Mingquan Wei^1, ,

1.
School of Mathematics and Stastics, Xinyang Normal University, Henan, Xinyang 464000, China

Corresponding author: Email: weimingquan11@mails.ucas.ac.cn(M. Wei)

Abstract

Abstract

In this paper, the author studies the boundedness for a large class of sublinear operators $ T_\alpha, \alpha\in[0, n) $ generated by Calderón-Zygmund operators ($ \alpha=0 $) and generated by fractional integral operator ($ \alpha>0 $) on generalized mixed Morrey spaces $ M^\varphi_{\vec{q}}({\mathbb R}^n) $. Moreover, the boundeness for commutators of $ T_\alpha, \alpha\in[0, n) $ on generalized mixed Morrey spaces $ M^\varphi_{\vec{q}}({\mathbb R}^n) $ is also studied. As applications, we obtain the boundedness for Hardy-Littlewood maximal operator, Calderón-Zygmund singular integral operators, fractional integral operator, fractional maximal operator and their commutators on generalzied mixed Morrey spaces.
- Generalized mixed Morrey spaces /
- sublinear operator /
- commutators /
- Hardy-Littlewood maximal operator /
- fractional integral operator
MSC: 42B20, 42B25, 42B35

FullText(HTML)

References

[1]	D. R. Adams, A note on Riesz potentials, Duke Math. J., 1975, 42(4), 765–778. Google Scholar
[2]	A. Benedek and R. Panzone, The space L^p, with mixed norm, Duke Math. J., 1961, 28(3), 301–324. Google Scholar
[3]	V. I. Burenkov and V. S. Guliyev, Necessary and sufficient conditions for the boundedness of the Riesz potential in local Morrey-type spaces, Potential Anal., 2009, 30(3), 211–249. Google Scholar
[4]	T. Chen and W. Sun, Iterated weak and weak mixed-norm spaces with applications to geometric inequalities, J. Geom. Anal., 2020, 30(4), 4268–4323. Google Scholar
[5]	F. Chiarenza, Morrey spaces and Hardy-Littlewood maximal function, Rend. Mat., 1987, 7, 273–279. Google Scholar
[6]	D. V. Cruz-Uribe, A. Fiorenza, J. Martell and C. Pérez, The boundedness of classical operators on variable L^p spaces, Ann. Acad. Sci. Fenn. Math., 2006, 31(1), 239–264. Google Scholar
[7]	D. V. Cruz-Uribe, J. M. Martell and C. Pérez, Weights, extrapolation and the theory of Rubio de Francia, In: Operator Theory: Advance and Applications, vol. 215, Birkhäuser, Basel, 2011. Google Scholar
[8]	L. Grafakos, Classical Fourier analysis, 2en edn, Springer, New York, 2008. Google Scholar
[9]	V. S. Guliev, Generalized weighted Morrey spaces and higher order commutators of sublinear operators, Eurasian Math. J., 2012, 3(3), 33–61. Google Scholar
[10]	V. Guliyev, M. Omarova, M. Ragusa and A. Scapellato, Regularity of solutions of elliptic equations in divergence form in modified local generalized Morrey spaces, Anal. Math. Phys., 2021, 11(1), 1–20. Google Scholar
[11]	V. S. Guliyev, Generalized local Morrey spaces and fractional integral operators with rough kernel, J. Math. Sci., 2013, 193(2), 211–227. Google Scholar
[12]	V. S. Guliyev, S. S. Aliyev, T. Karaman and P. S. Shukurov, Boundedness of sublinear operators and commutators on generalized Morrey spaces, Integral Equations and Operator Theory, 2011, 71(3), 327–355. Google Scholar
[13]	V. S. Guliyev and L. G. Softova, Global regularity in generalized Morrey spaces of solutions to nondivergence elliptic equations with VMO coefficients, Potential Anal., 2013, 38(3), 843–862. Google Scholar
[14]	K. P. Ho, Strong maximal operator on mixed-norm spaces, Ann. Univ. Ferrara Sez. VⅡ Sci. Mat., 2016, 62(2), 275–291. Google Scholar
[15]	K. P. Ho, Mixed norm lebesgue spaces with variable exponents and applications, Riv. Mat. Univ. Parma, 2018, 9(1), 21–44. Google Scholar
[16]	G. Lu, S. Lu and D. Yang, Singular integrals and commutators on homogeneous groups, Anal. Math., 2002, 28(2), 103–134. Google Scholar
[17]	S. Lu, Y. Ding and D. Yan, Singular integrals and related topics, World Scientific, Singapore, 2007. Google Scholar
[18]	C. B. Morrey, On the solutions of quasi-linear elliptic partial differential equations, Trans. Amer. Math. Soc., 1938, 43(1), 126–166. Google Scholar
[19]	B. Muckenhoupt and R. L. Wheeden, Norm inequalities for the littlewood-paley function g_λ^*, Trans. Amer. Math. Soc., 1974, 191, 95–111. Google Scholar
[20]	T. Nogayama, Boundedness of commutators of fractional integral operators on mixed Morrey spaces, Integral Transforms and Spec. Funct., 2019, 30(10), 790–816. Google Scholar
[21]	T. Nogayama, Mixed Morrey spaces, Positivity, 2019, 23(4), 961–1000. Google Scholar
[22]	T. Nogayama, T. Ono, D. Salim and Y. Sawano, Atomic decomposition for mixed Morrey spaces, J. Geom. Anal., 2021, 31(9), 9338–9365. Google Scholar
[23]	J. Peetre, On the theory of L_{p, λ} spaces, J. Funct. Anal., 1969, 4(1), 71–87. Google Scholar
[24]	M. Rosenthal and H. J. Schmeisser, On the boundedness of singular integrals in Morrey spaces and its preduals, J. Fourier Anal. Appl., 2016, 22(2), 462–490. Google Scholar
[25]	L. G. Softova, Parabolic oblique derivative problem with discontinuous coefficients in generalized Morrey spaces, Ric. Mat., 2013, 62(2), 265–278. Google Scholar
[26]	F. Soria and G. Weiss, A remark on singular integrals and power weights, Indiana Univ. Math. J., 1994, 43(1), 187–204. Google Scholar
[27]	J. Tan, Off-diagonal extrapolation on mixed variable Lebesgue spaces and its applications to strong fractional maximal operators, Georgian Math. J., 2020, 27(4), 637–647. Google Scholar
[28]	M. Yang, Z. Fu and J. Sun, Existence and large time behavior to coupled chemotaxis-fluid equations in Besov-Morrey spaces, J. Differential Equations, 2019, 266(9), 5867–5894. Google Scholar
[29]	H. Zhang and J. Zhou, The boundedness of fractional integral operators in local and global mixed Morrey-type spaces, Positivity, 2022, 26(1), 26. Google Scholar