Commutators of the fractional maximal function in generalized Morrey spaces on Carnot groups

References

• Morrey CB. On the solutions of quasi-linear elliptic partial differential equations. Trans Amer Math Soc. 1938;43:126–166.
   Web of Science ®Google Scholar
• Guliyev VS. Integral operators on function spaces on the homogeneous groups and on domains in Rn [Russian Doctor's degree dissertation]. Moscow: Mat Inst Steklov; 1994.
   Google Scholar
• Mizuhara T. Boundedness of some classical operators on generalized Morrey spaces. In: Igari S, editor. Harmonic analysis. Tokyo: Springer-Verlag; 1991. p. 183–189. (ICM 90 satellite proceedings).
   Google Scholar
• Nakai E. Hardy-Littlewood maximal operator, singular integral operators and Riesz potentials on generalized Morrey spaces. Math Nachr. 1994;166:95–103.
   Web of Science ®Google Scholar
• Guliyev VS. Function spaces, integral operators and two weighted inequalities on homogeneous groups, some applications. Baku: Casioglu; 1999. (Russian).
   Google Scholar
• Guliyev VS. Boundedness of the maximal, potential and singular operators in the generalized Morrey spaces. J Inequal Appl. 2009:1–20.
   Web of Science ®Google Scholar
• Guliyev VS, Guliyev RV, Omarova MN. Riesz transforms associated with Schrödinger operator on vanishing generalized Morrey spaces. Appl Comput Math. 2018;17(1):56–71.
   Web of Science ®Google Scholar
• Polidoro S, Ragusa MA. Sobolev-Morrey spaces related to an ultraparabolic equation. Manuscr Math. 1998;96(3):371–392.
   Web of Science ®Google Scholar
• Polidoro S, Ragusa MA. Harnack inequality for hypoelliptic ultraparabolic equations with a singular lower order term. Rev Mat Iberoamericana. 2008;24(3):1011–1046.
   Web of Science ®Google Scholar
• Sawano Y. A thought on generalized Morrey spaces. J Indonesian Math Soc. 2019;25(3):210–281.
   Web of Science ®Google Scholar
• Kaplan A. Fundamental solutions for a class of hypoelliptic PDE generated by composition of quadratics forms. Trans Amer Math Soc. 1980;258:147–153.
   Web of Science ®Google Scholar
• Deringoz F, Guliyev VS, Hasanov SG. Commutators of fractional maximal operator on generalized Orlicz-Morrey spaces. Positivity. 2018;22(1):141–158.
   Web of Science ®Google Scholar
• Zhang P, Wu J. Commutators of the fractional maximal function on variable exponent Lebesgue spaces. Czechoslovak Math J. 2014;64(1):183–197.
   Web of Science ®Google Scholar
• Bonfiglioli A, Lanconelli E, Uguzzoni F. Stratified Lie groups and potential theory for their sub-Laplacians. Berlin: Springer; 2007. (Springer monographs in mathematics).
   Google Scholar
• Folland GB, Stein EM. Hardy spaces on homogeneous groups. Princeton: Princeton Univ. Press; 1982. (Mathematical notes; vol. 28).
   Google Scholar
• Guliyev VS, Ekincioglu I, Kaya E, et al. Characterizations for the fractional maximal operator and its commutators in generalized Morrey spaces on Carnot groups. Integral Transforms Spec Funct. 2019;30(6):453–470.
   Web of Science ®Google Scholar
• Stein EM. Harmonic analysis: real-variable methods, orthogonality and oscillatory integrals. Princeton: Princeton Univ. Press; 1993.
   Google Scholar
• Armutcu H, Eroglu A, Isayev F. Characterizations for the fractional maximal operators on Carleson curves in local generalized Morrey spaces. Tbilisi Math J. 2020;13(1):23–38.
   Web of Science ®Google Scholar
• Guliyev VS, Sawano Y. Linear and sublinear operators on generalized Morrey spaces with non-doubling measures. Publ Math Debrecen. 2013;83(3):303–327.
   Web of Science ®Google Scholar
• Ibrahimov EJ, Dadashova GA, Ekincioglu SE. On the boundedness of the G-maximal operator and G-Riesz potential in the generalized G-Morrey spaces. Trans Natl Acad Sci Azerb Ser Phys.-Tech Math Sci Math. 2020;40(1):111–125.
   Google Scholar
• Rahimova KR. Characterizations of parabolic fractional integral operators on generalized parabolic Morrey spaces. Trans Natl Acad Sci Azerb Ser Phys-Tech Math Sci Mathematics. 2016;36(4):156–166.
   Google Scholar
• Eroglu A, Guliyev VS, Azizov CV. Characterizations for the fractional integral operators in generalized Morrey spaces on Carnot groups. Math Notes. 2017;102(5–6):722–734.
   Web of Science ®Google Scholar
• Eroglu A, Azizov JV, Guliyev VS. Fractional maximal operator and its commutators in generalized Morrey spaces on Heisenberg group. Proc Inst Math Mech Natl Acad Sci Azerb. 2018;44(2):304–317.
   Web of Science ®Google Scholar
• Eridani, Utoyo MI, Gunawan H. A characterization for fractional integrals on generalized Morrey spaces. Anal Theory Appl. 2012;28(3):263–268.
   Google Scholar
• Burenkov V, Gogatishvili A, Guliyev VS, et al. Boundedness of the fractional maximal operator in local Morrey-type spaces. Complex Var Elliptic Equ. 2010;55(8–10):739–758.
   Web of Science ®Google Scholar
• Guliyev VS, Akbulut A, Mammadov YY. Boundedness of fractional maximal operator and their higher order commutators in generalized Morrey spaces on Carnot groups. Acta Math Sci Ser B Engl Ed. 2013;33(5):1329–1346.
   Web of Science ®Google Scholar
• Guliyev VS, Shukurov PS. On the boundedness of the fractional maximal operator, Riesz potential and their commutators in generalized Morrey spaces. In: Advances in harmonic analysis and operator theory. Basel (AG): Birkhäuser/Springer; 2013. p. 175–199 (Oper theory adv appl.; 229).
   Google Scholar
• Sawano Y. Generalized Morrey spaces for non-doubling measures. Nonlinear Differ Equ Appl. 2008;15(4–5):413–425.
   Web of Science ®Google Scholar
• Akbulut A, Guliyev VS, Mustafayev R. On the boundedness of the maximal operator and singular integral operators in generalized Morrey spaces. Math Bohem. 2012;137(1):27–43.
   Google Scholar
• Nakai E. Orlicz-Morrey spaces and the Hardy-Littlewood maximal function. Stud Math. 2008;188(3):193–221.
   Web of Science ®Google Scholar
• Gunawan H. A note on the generalized fractional integral operators. J Indones Math Soc. 2003;9:39–43.
   Google Scholar
• Cruz-Uribe D, Fiorenza A. Endponit estimate and weighted norm inequalities for commutators of fractional integrals. Publ Mat. 2003;47:103–131.
   Web of Science ®Google Scholar