[1] Abbasova, M. M., Bandaliev, R. A.: On the boundedness of Hardy operator in the weighted variable exponent spaces. Proc. of Nat. Acad. of Sci. of Azerbaijan. Embedding theorems. Harmonic Analysis. 13 (2007), 5-17. MR 2719561

[2] Acerbi, E., Mingione, G.: Gradient estimates for a class of parabolic systems. Duke Math. J. 136 (2007), 285-320. DOI 10.1215/S0012-7094-07-13623-8 | MR 2286632 | Zbl 1113.35105

[3] Bandaliev, R. A.: On an inequality in Lebesgue space with mixed norm and with variable summability exponent. Mat. Zametki 84 (2008), 323-333 Russian. MR 2473750 | Zbl 1171.46023

[4] Bradley, J.: Hardy inequalities with mixed norms. Canadian Mathematical Bull. 21 (1978), 405-408. DOI 10.4153/CMB-1978-071-7 | MR 0523580 | Zbl 0402.26006

[5] Cruz-Uribe, D., Fiorenza, A., Neugebauer, C. J.: The maximal function on variable $L^p$ spaces. Ann. Acad. Sci. Fenn. Math. 28 (2003), 223-238. MR 1976842

[6] Diening, L.: Maximal function on generalized Lebesgue spaces $L^{p(\cdot)}$. Math. Inequal. Appl. 7 (2004), 245-253. MR 2057643

[7] Diening, L., Samko, S.: Hardy inequality in variable exponent Lebesgue spaces. Frac. Calc. and Appl. Anal. 10 (2007), 1-18. MR 2348863 | Zbl 1132.26341

[8] Edmunds, D. E., Kokilashvili, V.: Two-weighted inequalities for singular integrals. Canadian Math. Bull. 38 (1995), 295-303. DOI 10.4153/CMB-1995-043-5 | MR 1347301 | Zbl 0839.47022

[9] Edmunds, D. E., Kokilashvili, V., Meskhi, A.: On the boundedness and compactness of weighted Hardy operators in spaces $\smash{L^{p(x)}}$. Georgian Math. J. 12 (2005), 27-44. MR 2136721

[10] Edmunds, D. E., Kokilashvili, V., Meskhi, A.: Bounded and compact integral operators. Math. and Its Applications. 543, Kluwer Acad.Publish., Dordrecht (2002). MR 1920969 | Zbl 1023.42001

[11] Edmunds, D. E., Kokilashvili, V., Meskhi, A.: Two-weight estimates in $L^{p(x)}$ spaces for classical integral operators and applications to the norm summability of Fourier trigonometric series. Proc. A. Razmadze Math. Inst. 142 (2006), 123-128. MR 2294574

[12] Gadjiev, A. D., Aliev, I. A.: Weighted estimates for multidimensional singular integrals generated by a generalized shift operator. Mat. Sbornik 183 (1992), 45-66 Russian. MR 1198834

[13] Guliev, V. S.: Two-weight inequalities for integral operators in $L_p$-spaces and their applications. Trudy Mat. Inst. Steklov. 204 (1993), 97-116. MR 1320021

[14] Guliev, V. S.: Integral operators on function spaces defined on homogeneous groups and domains in $R^n.$ Doctor's dissertation. Mat. Inst. Steklov. (1994), 1-329.

[15] Harjulehto, P., Hästö, P., Koskenoja, M.: Hardy's inequality in a variable exponent Sobolev space. Georgian Math. J. 12 (2005), 431-442. MR 2174945 | Zbl 1096.46017

[16] Kokilashvili, V., Meskhi, A.: Two-weight inequalities for singular integrals defined on homogeneous groups. Proc. A. Razmadze Math. Inst. 112 (1997), 57-90. MR 1468962 | Zbl 0983.43501

[17] Kokilashvili, V., Samko, S. G.: Singular integrals in weighted Lebesgue space with variable exponent. Georgian Math. J. 10 (2003), 145-156. DOI 10.1515/GMJ.2003.145 | MR 1990694

[18] Kokilashvili, V., Samko, S. G.: The maximal operator in weighted variable spaces on metric measure space. Proc. A. Razmadze Math. Inst. 144 (2007), 137-144. MR 2387413

[19] Kopaliani, T. S.: On some structural properties of Banach function spaces and boundedness of certain integral operators. Czech. Math. J. 54 (2004), 791-805. DOI 10.1007/s10587-004-6427-3 | MR 2086735 | Zbl 1080.47040

[20] Kováčik, O., Rákosník, J.: On spaces $L^{p(x)}$ and $W^{k, p(x)}$. Czech. Math. J. 41 (1991), 592-618. MR 1134951

[21] Krbec, M., Opic, B., Pick, L., Rákosník, J.: Some recent results on Hardy type operators in weighted function spaces and related topics. Function spaces, differential operators and nonlinear analysis (Frie4ichroda, 1992). 158-184, Teubner-Texte Math., 133, Teubner, Stuttgart (1993). MR 1242582

[22] Lu, G., Lu, Sh., Yang, D.: Singular integrals and commutators on homogeneous groups. Analysis Math. 28 (2002), 103-134. DOI 10.1023/A:1016568918973 | MR 1918254 | Zbl 1026.43007

[23] Mashiyev, R. A., Çekiç, B., Mamedov, F. I., Ogras, S.: Hardy's inequality in power-type weighted $L^{p(\cdot)}(0, \infty)$ spaces. J. Math. Anal. Appl. 334 (2007), 289-298. DOI 10.1016/j.jmaa.2006.12.043 | MR 2332556

[24] Maz'ya, V. G.: Sobolev Spaces. Springer-Verlag, Berlin-Heidelberg-New York (1985). MR 0817985 | Zbl 0727.46017

[25] Muckenhoupt, B.: Hardy's inequality with weights. Studia Math. 44 (1972), 31-38. DOI 10.4064/sm-44-1-31-38 | MR 0311856 | Zbl 0236.26015

[26] Musielak, J.: Orlicz Spaces and Modular Spaces. Lecture Notes in Math. 1034. Springer-Verlag, Berlin-Heidelberg-New York (1983). MR 0724434 | Zbl 0557.46020

[27] Musielak, J., Orlicz, W.: On modular spaces. Studia Math. 18 (1959), 49-65. DOI 10.4064/sm-18-1-49-65 | MR 0101487 | Zbl 0099.09202

[28] Nakano, H.: Modulared semi-ordered linear spaces. Maruzen. Co., Ltd., Tokyo (1950). MR 0038565 | Zbl 0041.23401

[29] Nekvinda, A.: Hardy-Littlewood maximal operator in $L^{p(x)}(R^n)$. Math. Ineq. Appl. 7 (2004), 255-265. MR 2057644

[30] Opic, B., Kufner, A.: Hardy-Type Inequalities. Pitman Research Notes in Math. ser., 219. Longman sci. and tech., Harlow (1990). MR 1069756 | Zbl 0698.26007

[31] Orlicz, W.: Über konjugierte Exponentenfolgen. Studia Math. 3 (1931), 200-212. DOI 10.4064/sm-3-1-200-211 | Zbl 0003.25203

[32] Růžička, M.: Electrorheological Fluids: Modeling and Mathematical theory. Lecture Notes in Math. 1748. Springer-Verlag, Berlin (2000). MR 1810360

[33] Samko, S. G.: Differentiation and integration of variable order and the spaces $L^{p(x)}$. Proc.Inter.Conf. "Operator theory for Complex and Hypercomplex analysis". 1994, 203-219. Contemp. Math., 212, AMS, Providence, RI, 1998. MR 1486602

[34] Samko, S. G.: Convolution type operators in $L^{p(x)}$. Integ. Trans. and Special Funct. 7 (1998), 123-144. DOI 10.1080/10652469808819191 | MR 1658190

[35] Sharapudinov, I. I.: On a topology of the space $L^{p(t)}([0,1])$. Mat. Zametki 26 (1979), 613-637 Russian. MR 0552723

[36] Sharapudinov, I. I.: The basis property of the Haar system in the space $L^{p(t)}([0,1])$ and the principle of localization in the mean. Mat. Sbornik 130 (1986), 275-283 Russian. MR 0854976

[37] Soria, F., Weiss, G.: A remark on singular integrals and power weights. Indiana Univ. Math. J. 43 (1994), 187-204. DOI 10.1512/iumj.1994.43.43009 | MR 1275458 | Zbl 0803.42004

[38] Zeren, Y., Guliyev, V. S.: Two-weight norm inequalities for some anisotropic sublinear operators. Turkish Math. J. 30 (2006), 329-350. MR 2248753 | Zbl 1179.42015

[39] Zhikov, V. V.: Averaging of functionals of the calculus of variations and elasticity theory. Izv. Akad. Nauk Russian 50 (1986), 675-710 Russian. MR 0864171 | Zbl 0599.49031