Riesz potential in the local Morrey–Lorentz spaces and some applications

References

[1] J. Alvarez, J. Lakey and M. Guzmán-Partida, Spaces of bounded λ-central mean oscillation, Morrey spaces, and λ-central Carleson measures, Collect. Math. 51 (2000), no. 1, 1–47. Suche in Google Scholar

[2] K. F. Andersen and B. Muckenhoupt, Weighted weak type Hardy inequalities with applications to Hilbert transforms and maximal functions, Studia Math. 72 (1982), no. 1, 9–26. 10.4064/sm-72-1-9-26Suche in Google Scholar

[3] C. Aykol, V. S. Guliyev, A. Kucukaslan and A. Serbetci, The boundedness of Hilbert transform in the local Morrey–Lorentz spaces, Integral Transforms Spec. Funct. 27 (2016), no. 4, 318–330. 10.1080/10652469.2015.1121483Suche in Google Scholar

[4] C. Aykol, V. S. Guliyev and A. Serbetci, Boundedness of the maximal operator in the local Morrey–Lorentz spaces, J. Inequal. Appl. 2013 (2013), Paper No. 346. 10.1186/1029-242X-2013-346Suche in Google Scholar

[5] C. Bennett and R. Sharpley, Interpolation of Operators, Pure Appl. Math. 129, Academic Press, Boston, 1988. Suche in Google Scholar

[6] V. I. Burenkov, H. V. Guliyev and V. S. Guliyev, Necessary and sufficient conditions for the boundedness of fractional maximal operators in local Morrey-type spaces, J. Comput. Appl. Math. 208 (2007), no. 1, 280–301. 10.1016/j.cam.2006.10.085Suche in Google Scholar

[7] 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. 30 (2009), no. 3, 211–249. 10.1007/s11118-008-9113-5Suche in Google Scholar

[8] V. I. Burenkov, V. S. Guliyev, A. Serbetci and T. V. Tararykova, Necessary and sufficient conditions for the boundedness of genuine singular integral operators in local Morrey-type spaces, Eurasian Math. J. 1 (2010), no. 1, 32–53. 10.1134/S1064562408050025Suche in Google Scholar

[9] A.-P. Calderón, Spaces between L1 and L∞ and the theorem of Marcinkiewicz, Studia Math. 26 (1966), 273–299. 10.4064/sm-26-3-301-304Suche in Google Scholar

[10] F. Chiarenza and M. Frasca, Morrey spaces and Hardy–Littlewood maximal function, Rend. Mat. Appl. (7) 7 (1987), no. 3–4, 273–279. Suche in Google Scholar

[11] G. Di Fazio and M. A. Ragusa, Commutators and Morrey spaces, Boll. Unione Mat. Ital. A (7) 5 (1991), no. 3, 323–332. Suche in Google Scholar

[12] V. S. Guliyev, Integral operators on function spaces on the homogeneous groups and on domains in ℝn, (in Russian), Doctor’s degree dissertation, Steklov Mathematical Institute, Moscow, 1994. Suche in Google Scholar

[13] V. S. Guliyev, Function Spaces, Integral Operators and Two Weighted Inequalities on Homogeneous Groups. Some Applications (in Russian), Elm, Baku, 1999. Suche in Google Scholar

[14] V. S. Guliyev, C. Aykol, A. Kucukaslan and A. Serbetci, Maximal operator and Calderon–Zygmund operators in local Morrey–Lorentz spaces, Integral Transforms Spec. Funct. 27 (2016), no. 11, 866–877. 10.1080/10652469.2016.1227329Suche in Google Scholar

[15] V. S. Guliyev, A. Serbetci and I. Ekincioglu, Necessary and sufficient conditions for the boundedness of rough B-fractional integral operators in the Lorentz spaces, J. Math. Anal. Appl. 336 (2007), no. 1, 425–437. 10.1016/j.jmaa.2007.02.080Suche in Google Scholar

[16] K.-P. Ho, Sobolev–Jawerth embedding of Triebel–Lizorkin–Morrey–Lorentz spaces and fractional integral operator on Hardy type spaces, Math. Nachr. 287 (2014), no. 14–15, 1674–1686. 10.1002/mana.201300217Suche in Google Scholar

[17] S. Lu, Y. Ding and D. Yan, Singular Integrals and Related Topics, World Scientific, Hackensack, 2007. 10.1142/6428Suche in Google Scholar

[18] G. Mingione, Gradient estimates below the duality exponent, Math. Ann. 346 (2010), no. 3, 571–627. 10.1007/s00208-009-0411-zSuche in Google Scholar

[19] R. O’Neil, Convolution operators and L⁢(p,q) spaces, Duke Math. J. 30 (1963), 129–142. 10.1215/S0012-7094-63-03015-1Suche in Google Scholar

[20] M. A. Ragusa, Embeddings for Morrey–Lorentz spaces, J. Optim. Theory Appl. 154 (2012), no. 2, 491–499. 10.1007/s10957-012-0012-ySuche in Google Scholar

[21] N. Samko, Weighted Hardy and singular operators in Morrey spaces, J. Math. Anal. Appl. 350 (2009), no. 1, 56–72. 10.1016/j.jmaa.2008.09.021Suche in Google Scholar

[22] N. Samko, Weighted Hardy and potential operators in Morrey spaces, J. Funct. Spaces Appl. 2012 (2012), Article ID 678171. 10.1155/2012/678171Suche in Google Scholar

[23] E. Sawyer, Boundedness of classical operators on classical Lorentz spaces, Studia Math. 96 (1990), no. 2, 145–158. 10.4064/sm-96-2-145-158Suche in Google Scholar

[24] E. M. Stein, On the functions of Littlewood–Paley, Lusin, and Marcinkiewicz, Trans. Amer. Math. Soc. 88 (1958), 430–466. 10.1090/S0002-9947-1958-0112932-2Suche in Google Scholar

[25] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Math. Ser. 30, Princeton University Press, Princeton, 1970. 10.1515/9781400883882Suche in Google Scholar