References (49)
Acquistapace, P.: On BMO regularity for linear elliptic systems. Ann. Mat. Pura Appl. 161, 231-270 (1992)Akbulut, A., Guliyev, V.S., Mustafayev, R.: On the boundedness of the maximal operator and singular integral operators in generalized Morrey spaces. Math. Bohem. 137(1), 27-43 (2012)Bennett, C., Sharpley, R.: Interpolation of Operators. Academic Press, Boston (1988)Bramanti, M., Cerutti, M.C.: W 1,2 p solvability for the Cauchy-Dirichlet problem for parabolic equations with V M O coefficients. Commun. Partial Differ. Equ. 18, 1735-1763 (1993)Burenkov, V.I., Chigambayeva, D.K., Nursultanov, E.D.: Marcinkiewicz-type interpolation theorem and estimates for convolutions for Morrey-type spaces. Eurasian Math. J. 9(2), 82-88 (2018)Burenkov, V.I., Gogatishvili, A., Guliyev, V.S., Mustafayev, R.: Boundedness of the fractional maximal operator in local Morrey-type spaces. Complex Var. Elliptic Equ. 55(8-10), 739-758 (2010)Byun, S., Lee, M.: Weighted estimates for nondivergence parabolic equations in Orlicz spaces. J. Funct. Anal. 268, 2530-2563 (2015)Calderón, A.P., Zygmund, A.: On the existence of certain singular integrals. Acta. Math. 88, 85-139 (1952)Calderón, A.P., Zygmund, A.: Singular integral operators and differential equations. Am. J. Math. 79, 901-921 (1957)Chiarenza, F., Frasca, M., Longo, P.: Interior W 2, p -estimates for nondivergence ellipic equations with discontinuous coefficients. Ricerche Mat. 40, 149-168 (1991)Chiarenza, F., Frasca, M., Longo, P.: W 2, p -solvability of Dirichlet problem for nondivergence ellipic equations with VMO coefficients. Trans. Am. Math. Soc. 336, 841-853 (1993)Di Fazio, G., Ragusa, M.A.: Interior estimates in Morrey spaces for strong solutions to nondivergence form equations with discontinuous coefficients. J. Funct. Anal. 112(3), 241-256 (1993)Di Fazio, G., Palagachev, D.K., Ragusa, M.A.: Global Morrey regularity of strong solutions to the Dirichlet problem for elliptic equations with discontinuous coefficients. J. Funct. Anal. 166(2), 179- 196 (1999)Di Fazio, G., Hakim, D.I., Sawano, Y.: Elliptic equations with discontinuous coefficients in generalized Morrey spaces. Eur. J. Math. 3(3), 728-762 (2017)Dong, H., Kim, D.: Parablic and elliptic systems in divergence form with variably partially BMO coefficients. SIAM J. Math. Anal. 43, 1075-1098 (2011)Fabes, E.B., Rivière, N.: Singular integrals with mixed homogeneity. Stud. Math. 27, 19-38 (1966)Fan, D., Lu, S., Yang, D.: Regularity in Morrey spaces of strong solutions to nondivergence elliptic equations with VMO coefficients. Georgian Math. J. 5, 425-440 (1998)Gilbarg, G., Trudinger, N.S.: Elliptic Partial Differential Equations of Second Order, 2nd edn. Springer, Berlin (1983)Guliyev, V.S.: Integral operators on function spaces on the homogeneous groups and on domains in R n . Doctor's degree dissertation, Mat. Inst. Steklov, Moscow (1994) (in Russian)Guliyev, V.S.: Function spaces, integral operators and two weighted inequalities on homogeneous groups. Some Applications. Casioglu, Baku (1999) (in Russian)Guliyev, V.S.: Boundedness of the maximal, potential and singular operators in the generalized Morrey spaces. J. Inequal. Appl. Art. ID 503948 (2009)Guliyev, V.S.: Local generalized Morrey spaces and singular integrals with rough kernel. Azerb. J. Math. 3(2), 79-94 (2013)Guliyev, V.S.: Generalized local Morrey spaces and fractional integral operators with rough kernel. J. Math. Sci. (N. Y.) 193(2), 211-227 (2013)Guliyev, V.S., Deringoz, F.: On the Riesz potential and its commutators on generalized Orlicz-Morrey spaces. J. Funct. Spaces Appl., Article ID 617414 (2014)Guliyev, V.S., Softova, L.: Global regularity in generalized weighted Morrey spaces of solutions to nondivergence elliptic equations with VMO coefficients. Potential Anal. 38(4), 843-862 (2013)Guliyev, V.S., Softova, L.: Generalized Morrey regularity for parabolic equations with discontinuity data. Proc. Edinb. Math. Soc. (2) 58(1), 199-218 (2015)Guliyev, V.S., Omarova, M.N., Ragusa, M.A., Scapellato, A.: Commutators and generalized local Morrey spaces. J. Math. Anal. Appl. 457(2), 1388-1402 (2018)Guliyev, V.S., Ahmadli, A.A. Omarova, M.N., Softova, L.G.: Global regularity in Orlicz-Morrey spaces of solutions to nondivergence elliptic equations with VMO coefficients. Electron. J. Differ. Equ., Paper No. 110 (2018)Jia, H., Li, D., Wang, L.: Regularity in Orlicz spaces for the Poisson equation. Manuscr. Math. 122, 265-275 (2007)John, F., Nirenberg, L.: On functions of bounded mean osillation. Commun. Pure Appl. Math. 14, 415-426 (1961)Jones, P.W.: Extension theorems for BMO. Indiana Univ. Math. J. 29, 41-66 (1980)Kokilashvili, V., Krbec, M.M.: Weighted Inequalities in Lorentz and Orlicz Spaces. World Scientific, Singapore (1991)Krylov, N.V.: Parabolic and elliptic equations with VMO coefficients. Commun. Partial. Differ. Equ. 32, 453-475 (2007)Ladyzhenskaya, O.A., Solonnikov, V.A., Ural'tseva, N.N.: Linear and Quasilinear Equations of Parabolic Type. Transl. Math. Monographs 23, American Mathematical Society, Providence (1968)Krasnoselskii, M.A., Rutickii, Ya.B.: Convex functions and Orlicz spaces. English translation P. Noord- hoff Ltd., Groningen (1961)Liu, P., Hou, Y., Wang, M.: Weak Orlicz space and its applications to the martingale theory. Sci. China Math. 53(4), 905-916 (2010)Maugeri, A., Palagachev, D.K., Softova, L.G.: Elliptic and Parabolic Equations with Discontinuous Coefficients. Wiley-VCH, Berlin (2000)Mizuhara, T.: Boundedness of some classical operators on generalized Morrey spaces. Harmonic Analysis, Proceedings Conference, Sendai/Japan 1990, ICM-90 Satellite Conference Proceedings, pp 183-189 (1991)Morrey, C.B.: On the solutions of quasi-linear elliptic partial differential equations. Trans. Am. Math. Soc. 43, 126-166 (1938)Nakai, E.: Hardy-Littlewood maximal operator, singular integral operators and the Riesz potentials on generalized Morrey spaces. Math. Nachr. 166, 95-103 (1994)Palagachev, D., Softova, L.: Fine regularity for elliptic systems with discontinuous ingredients. J. Arch. Math. 86(2), 145-153 (2006)Persson, L.E., Samko, N.: Weighted Hardy and potential operators in the generalized Morrey spaces. J. Math. Anal. Appl. 377(2), 792-806 (2011)Rao, M.M., Ren, Z.D.: Theory of Orlicz Spaces. M. Dekker Inc., New York (1991)Radulescu, V.D., Repovs, D.D.: Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis. Monographs and Research Notes in Mathematics. CRC Press, Boca Raton (2015)Sarason, D.: On functions of vanishes mean oscillation. Trans. Am. Math. Soc. 207, 391-405 (1975)Sawano, Y.: Theory of Besov spaces. Developments in Mathematics, vol. 56. Springer, Singapore (2018)Sawano, Y.: A thought on generalized Morrey spaces. J. Indonesian Math. Soc. 25(3), 210-281 (2019)Softova, L.: Morrey-type regularity of solutions to parabolic problems with discontinuous data. Manuscr. Math. 136(3-4), 365-382 (2011)Weiss, G.: A note on Orlicz spaces. Port. Math. 15, 35-47 (1956)
