Document Zbl 1513.42049

Calderón-Zygmund operators with kernels of Dini’s type and their multilinear commutators on generalized Morrey spaces. (English) Zbl 1513.42049

Trans. Natl. Acad. Sci. Azerb., Ser. Phys.-Tech. Math. Sci. 41, No. 4, Math., 100-111 (2021).

Summary: In this paper, we obtain the endpoint boundedness for the Calderón-Zygmund operators with kernels of Dini’s type on generalized Morrey spaces. We also get similar results for the multilinear commutators of Calderón-Zygmund operators with kernels of Dini’s type with \(BMO\) functions.

Cited in 6 Documents

MSC:

42B20	Singular and oscillatory integrals (Calderón-Zygmund, etc.)
42B35	Function spaces arising in harmonic analysis

Keywords:

generalized Morrey spaces; Calderón-Zygmund operator; commutator; BMO

Cite Review PDF

Full Text: Link

References:

[1]	Akbulut, A., Burenkov, V.I., Guliyev, V.S.: Anisotropic fractional maximal commuta-tors with BM O functions on anisotropic morrey-type spaces, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci. 40(4), Mathematics, 13-32 (2020). · Zbl 1513.42071
[2]	Calderon, A.P.: Commutators of singular integral operators, Proc. Natl. Acad. Sci. USA, 53, 1092-1099 (1965). · Zbl 0151.16901
[3]	Calderon, A.P.: Cauchy integrals on Lipschitz curves and related operators, Proc. Natl. Acad. Sci. USA, 74(4), 1324-1327 (1977). · Zbl 0373.44003
[4]	Coifman, R.R., Meyer, Y.: Au delà des Opérateurs Pseudo-Différentiels, Astérisque 57. Société Maématique de France, Paris, France, (1978). · Zbl 0483.35082
[5]	Eroglu, A., Azizov, J.V.: A note on the fractional integral operators in generalized Morrey spaces on the Heisenberg group, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci. 37(1), Mathematics, 86-91 (2017). · Zbl 1513.42038
[6]	Eroglu, A., Isayev, F.A., Namazov, F.M.: Fractional integral associated to Schrödinger operator on the Heisenberg groups in vanishing generalized Morrey spaces, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci., 38(4), Mathematics, 54-62 (2018). · Zbl 1412.22021
[7]	Giaquinta, M.: Multiple integrals in the calculus of variations and nonlinear elliptic systems, Princeton Univ. Press, Princeton, NJ, 1983. · Zbl 0516.49003
[8]	Guliyev, V.S.: Integral operators on function spaces on the homogeneous groups and on domains in R n , Doctoral dissertation, Moscow, Mat. Inst. Steklov, 329 pp. (1994) (in Russian).
[9]	Guliyev, V.S.: Function spaces, integral operators and two weighted inequalities on homogeneous groups. Some applications, Baku, Elm. 332 pp. (1999) (Russian).
[10]	Guliyev, V.S.: Boundedness of the maximal, potential and singular operators in the generalized Morrey spaces, J. Inequal. Appl. Art. ID 503948, 20 pp. (2009). · Zbl 1193.42082
[11]	Guliyev, V.S.: Generalized weighted Morrey spaces and higher order commutators of sublinear operators, Eurasian Math. J. 3(3), 33-61 (2012). · Zbl 1271.42019
[12]	Guliyev, V.S.: Generalized local Morrey spaces and fractional integral operators with rough kernel, J. Math. Sci., (N. Y.) 193(2), 211-227 (2013). · Zbl 1277.42021
[13]	Guliyev, V.S., Ismayilova, A.F.: Multi-sublinear maximal operator and multilinear sin-gular integral operators on generalized Morrey spaces, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb. 40(2), 65-77 (2014). · Zbl 1388.42037
[14]	Guliyev, V.S., Guliyev, R.V., Omarova, M.N.: Riesz transforms associated with Schrödinger operator on vanishing generalized Morrey spaces, Appl. Comput. Math. 17(1), 56-71 (2018). · Zbl 1452.42013
[15]	Guliyev, V.S., Akbulut, A., Celik, S., Omarova, M.N.: Higher order Riesz transforms related to Schrödinger type operator on local generalized Morrey spaces, TWMS Jour. Pure Appl. Math. 10(1), 58-75 (2019). · Zbl 1422.42032
[16]	Hasanov, A.A.: (p, p)-admissible multi-sublinear singular integral operators in product generalized local Morrey spaces, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci., 40(4), Mathematics, 85-96 (2020). · Zbl 1513.42042
[17]	Ibrahimov, E.J., Dadashova, G.A., Ekincioglu, S.E.: 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., 40(1), Mathematics, 111-125 (2020). · Zbl 1513.42077
[18]	Ismayilova, A.F., Isayev, F.A.: Multi-sublinear operators generated by multilinear Calderón-Zygmund operators on product generalized Morrey spaces, Trans. Natl. · Zbl 1513.42050
[19]	Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci., 40(4), Mathematics, 110-117 (2020).
[20]	Kufner, A., John, O., Fuçik, S.: Function Spaces, Noordhoff International Publishing: Leyden, Publishing House Czechoslovak Academy of Sciences: Prague, (1977). · Zbl 0364.46022
[21]	Lin, Y.: Strongly singular Calderón-Zygmund operator and commutator on Morrey type spaces, Acta Math. Sin. (Engl. Ser.) 23(11), 2097-2110 (2007). · Zbl 1131.42014
[22]	Lin, Y., Lu, Sh.: Strongly singular Calderón-Zygmund operators and their commuta-tors, Jordan Journal of Mathematics and Statistics, 1(1), 31-49 (2008). · Zbl 1279.42018
[23]	Liu, Z.G., Lu, S.Z.: Endpoint estimates for commutators of Calderón-Zygmund type operators, Kodai Math. J., 25(1), 79-88 (2002). · Zbl 1003.42010
[24]	Morrey, C.B.: On the solutions of quasi-linear elliptic partial differential equations, Trans. Amer. Math. Soc., 43, 126-166 (1938). · JFM 64.0460.02
[25]	Mizuhara, T.: Boundedness of some classical operators on generalized Morrey spaces, Harmonic Analysis (Sendai, 1990), S. Igari, Ed, ICM 90 Satellite Conference Proceed-ings, Springer, Tokyo, Japan, pp. 183-189 (1991). · Zbl 0771.42007
[26]	Nakai, E.: Hardy-Littlewood maximal operator, singular integral operators and Riesz potentials on generalized Morrey spaces, Math. Nachr. 166, 95-103 (1994). · Zbl 0837.42008
[27]	Quek, T., Yang, D.: Calderón-Zygmund-type operators on weighted weak Hardy spaces over R n , Acta Math. Sin. (Engl. Ser.), 16(1), 141-160 (2000). · Zbl 0956.42011
[28]	Sawano, Y.: A thought on generalized Morrey spaces, J. Indonesian Math. Soc., 25(3), 210-281 (2019). · Zbl 1451.26032
[29]	Stein, E.M.: Harmonic Analysis: Real Variable Methods, Orthogonality and Oscilla-tory Integrals, vol. 43 of Princeton Mathematical Series, Princeton University Press, Princeton, NJ, USA, (1993). · Zbl 0821.42001
[30]	Wang, H.: Boundedness of θ-type Calderón-Zygmund operators and commutators in the genralized weighted Morrey spaces, J. Funct. Spaces, Art. ID 1309348, 18 pp. (2016). · Zbl 1352.42023
[31]	Zhang, P., Sun J.: Commutators of multilinear Calderón-Zygmund operators with ker-nels of Dini’s type and applications, J. Math. Inequal. 13(4), 1071-1093 (2019). · Zbl 1434.42026
[32]	Yabuta, K.: Generalizations of Calderón-Zygmund operators, Studia Math. 82, 17-31 (1985). · Zbl 0585.42012

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.