Some notes on commutators of the fractional maximal and Riesz potential operators on Orlicz spaces

The main focus of this paper is commutators and maximal commutators on Orlicz spaces for fractional maximal functions and Riesz potential. The main advance in comparison with the existing results is that we manage to obtain conditions for the boundedness in less restrictive terms

Fractional maximal function and its commutators on Orlicz spaces

In this paper, we find necessary and sufficient conditions for the boundedness of fractional maximal operator $M_{\alpha}$ on Orlicz spaces. As an application of this results we consider the boundedness of fractional maximal commutator $M_{b,\alpha}$ and nonlinear commutator of fractional maximal operator $[b,M_{\alpha}]$ on Orlicz spaces, when $b$ belongs to the Lipschitz space, by which some new characterizations of the Lipschitz spaces are given.Comment: 15 pages, Anal. Math. Phys.(to appear

A characterization for Adams-type boundedness of the fractional maximal operator on generalized Orlicz-Morrey spaces

WOS: 000399466500003In the present paper, we shall give a characterization for weak/strong Adams-type boundedness of the fractional maximal operator on generalized Orlicz-Morrey spaces.Ahi Evran University Scientific Research ProjectAhi Evran University [FEF.A3.16.024]; grant of Presidium Azerbaijan National Academy of ScienceAzerbaijan National Academy of Sciences (ANAS)The research of V.S. Guliyev and F. Deringoz is partially supported by the grant of Ahi Evran University Scientific Research Project (FEF.A3.16.024). The research of V.S. Guliyev is partially supported by the grant of Presidium Azerbaijan National Academy of Science 2015. We thank the referee(s) for careful reading the paper and useful comments

Commutators of fractional maximal operator on generalized Orlicz-Morrey spaces

WOS: 000425301900011In the present paper, we shall give necessary and sufficient conditions for the Spanne and Adams type boundedness of the commutators of fractional maximal operator on generalized Orlicz-Morrey spaces, respectively. The main advance in comparison with the existing results is that we manage to obtain conditions for the boundedness not in integral terms but in less restrictive terms of supremal operators.Ahi Evran UniversityAhi Evran University [FEF.A3.16.024]; Ministry of Education and Science of the Russian FederationMinistry of Education and Science, Russian Federation [02.a03.21.0008]The research of V.S. Guliyev and F. Deringoz is partially supported by the grant of Ahi Evran University Scientific Research Project (FEF.A3.16.024). The research of V.S. Guliyev is partially supported by the Ministry of Education and Science of the Russian Federation (the Agreement No. 02.a03.21.0008)

Non-smooth Atomic Decompositions for Generalized Orlicz-Morrey Spaces of the Third Kind

WOS: 000382700200006We deal with the generalized Orlicz-Morrey space of the third kind and consider the decomposition method. Also we characterize its predual space. Some maximal estimates for generalized Orlicz-Morrey spaces of the third kind are also obtained by using the weighted Hardy operators. As an application, we consider the Olsen inequality, which is a bilinear estimate on the fractional integral operator. As an appendix, we consider a general form of the vector-valued boundedness of the Hardy-Littlewood maximal operator, where in the definition of depends on as well. This paper contains a remedy for the mistake in the proof of the Olsen inequality of the 2014 paper by the second author (Iida et al. in Z. Anal. Anwend. 33(2):149-170, 2014).Science Development Foundation under the President of the Republic of AzerbaijanScience Development Foundation (SDF) - Azerbaijan [EIF-2013-9(15)-46/10/1]; Presidium Azerbaijan National Academy of ScienceAzerbaijan National Academy of Sciences (ANAS)The research of V. Guliyev was partially supported by the grant of Science Development Foundation under the President of the Republic of Azerbaijan, Grant EIF-2013-9(15)-46/10/1 and by the grant of Presidium Azerbaijan National Academy of Science 2015. This paper is written during the stay of Y. Sawano in Ahi Evran University. Y. Sawano is thankful to Ahi Evran University for this support of the stay there. Y. Sawano is thankful to Professor Jie Xiao for his pointing out that (7.18) is correct under some restricted conditions. The authors are thankful to Professor Mitsuo Izuki at Okayama University for his careful reading of the manuscript

A characterization for Adams-type boundedness of the fractional maximal operator on generalized Orlicz-Morrey spaces

WOS: 000399466500003In the present paper, we shall give a characterization for weak/strong Adams-type boundedness of the fractional maximal operator on generalized Orlicz-Morrey spaces.Ahi Evran University Scientific Research ProjectAhi Evran University [FEF.A3.16.024]; grant of Presidium Azerbaijan National Academy of ScienceAzerbaijan National Academy of Sciences (ANAS)The research of V.S. Guliyev and F. Deringoz is partially supported by the grant of Ahi Evran University Scientific Research Project (FEF.A3.16.024). The research of V.S. Guliyev is partially supported by the grant of Presidium Azerbaijan National Academy of Science 2015. We thank the referee(s) for careful reading the paper and useful comments

Decompositions of local Morrey-type spaces

WOS: 000408222400026We develop and apply a decomposition theory for generic local Morrey-type spaces. Our result is nonsmooth decomposition, which follows from the fact that local Morrey-type spaces are isomorphic to Hardy local Morrey-type spaces in the generic case. As an application of our results, we consider the Hardy operator.Science Development Foundation under Republic of AzerbaijanScience Development Foundation (SDF) - Azerbaijan [EIF-2013-9(15)-46/10/1]; Presidium Azerbaijan National Academy of ScienceAzerbaijan National Academy of Sciences (ANAS); [24540194]Yoshihiro Sawano was supported by Grant-in-Aid for Scientific Research (C), No. 24540194. The research of V. Guliyev was partially supported by the grant of Science Development Foundation under the President of the Republic of Azerbaijan, Grant EIF-2013-9(15)-46/10/1 and by the grant of Presidium Azerbaijan National Academy of Science 2015. The authors are grateful to Dr. Denny Ivanal Hakim for his pointing out our mistake in Section 4

Maximal Operator and its Commutators on Generalized Weighted Orlicz-Morrey Spaces

WOS: 000457878700002In the present paper, we shall give necessary and sufficient conditions for the boundedness of the Hardy-Littlewood maximal operator and its commutators on generalized weighted Orlicz-Morrey spaces M-w(Phi,psi)(R-n). The main advance in comparison with the existing results is that we manage to obtain conditions for the boundedness not in integral terms but in less restrictive terms of supremal operators and we do not need Delta(2)-condition for the boundedness of the maximal operator. We also consider the vector-valued boundedness of the Hardy-Littlewood maximal operator

Riesz potential and its commutators on Orlicz spaces

WOS: 000401058200002PubMed ID: 28469352In the present paper, we shall give necessary and sufficient conditions for the strong and weak boundedness of the Riesz potential operator I-alpha on Orlicz spaces. Cianchi (J. Lond. Math. Soc. 60(1): 247-286, 2011) found necessary and sufficient conditions on general Young functions Phi and Psi ensuring that this operator is of weak or strong type from L-Phi into L-Psi. Our characterizations for the boundedness of the above-mentioned operator are different from the ones in (Cianchi in J. Lond. Math. Soc. 60(1): 247-286, 2011). As an application of these results, we consider the boundedness of the commutators of Riesz potential operator [b,I-alpha] on Orlicz spaces when b belongs to the BMO and Lipschitz spaces, respectively.Ahi Evran University Scientific Research ProjectAhi Evran University [FEF.A3.16.011]; Ministry of Education and Science of the Russian FederationMinistry of Education and Science, Russian Federation [02.a03.21.0008]The research of F Deringoz was partially supported by the grant of Ahi Evran University Scientific Research Project (FEF.A3.16.011). The research of VS Guliyev was partially supported by the Ministry of Education and Science of the Russian Federation (Agreement number: 02.a03.21.0008)

Fractional maximal function and its commutators on Orlicz spaces

WOS: 000463591800012In this paper, we find necessary and sufficient conditions for the boundedness of fractional maximal operator M on Orlicz spaces. As an application of this results we consider the boundedness of fractional maximal commutator Mb, and nonlinear commutator of fractional maximal operator [b,M] on Orlicz spaces, when b belongs to the Lipschitz space, by which some new characterizations of the Lipschitz spaces are given.Presidium of Azerbaijan National Academy of ScienceAzerbaijan National Academy of Sciences (ANAS); Ministry of Education and Science of the Russian FederationMinistry of Education and Science, Russian Federation [02, a03.21.0008]The research of V.S. Guliyev was partially supported by the grant of Presidium of Azerbaijan National Academy of Science 2015 and by the Ministry of Education and Science of the Russian Federation (the Agreement No. 02.a03.21.0008)