[1] Bloom S., Kerman R., Weighted Orlicz space integral inequalities for the Hardy-Littlewood maximal operator, Studia Math., 1994, 110(2), 149–167 Google Scholar

[2] Bobkov S.G., Götze F., Exponential integrability and transportation cost related to logarithmic Sobolev inequalities, J. Funct. Anal., 1999, 163(1), 1–28 http://dx.doi.org/10.1006/jfan.1998.3326CrossrefGoogle Scholar

[3] Brandolini B., Chiacchio F., Trombetti C., Hardy type inequalities and Gaussian measure, Commun. Pure Appl. Anal., 2007, 6(2), 411–428 http://dx.doi.org/10.3934/cpaa.2007.6.411CrossrefGoogle Scholar

[4] Brown R.C., Hinton D.B., Interpolation inequalities with power weights for functions of one variable, J. Math. Anal. Appl., 1993, 172(1), 233–242 http://dx.doi.org/10.1006/jmaa.1993.1020CrossrefGoogle Scholar

[5] Brown R.C., Hinton D.B., Weighted interpolation and Hardy inequalities with some spectral-theoretic applications, In: Proceedings of the Fourth International Colloquium on Differential Equations, Plovdiv, August 18–23, 1993, VSP, Utrecht, 1994, 55–70 Google Scholar

[6] Caffarelli L., Kohn R., Nirenberg L., First order interpolation inequalities with weights, Compositio Math., 1984, 53(3), 259–275 Google Scholar

[7] Chua S.-K., On weighted Sobolev interpolation inequalities, Proc. Amer. Math. Soc., 1994, 121(2), 441–449 http://dx.doi.org/10.1090/S0002-9939-1994-1221721-4CrossrefGoogle Scholar

[8] Chua S.-K., Sharp conditions for weighted Sobolev interpolation inequalities, Forum Math., 2005, 17(3), 461–478 http://dx.doi.org/10.1515/form.2005.17.3.461CrossrefGoogle Scholar

[9] Cianchi A., Some results in the theory of Orlicz spaces and applications to variational problems, In: Nonlinear Analysis, Function Spaces and Applications, 6, Prague, May 31–June 6, 1998, Academy of Sciences of the Czech Republic, Mathematical Institute, Prague, 1999, 50–92 Google Scholar

[10] Fernández-Martínez P., Signes T., Real interpolation with symmetric spaces and slowly varying functions, Q. J. Math., 2012, 63(1), 133–164 http://dx.doi.org/10.1093/qmath/haq009CrossrefGoogle Scholar

[11] Fiorenza A., Krbec M., Indices of Orlicz spaces and some applications, Comment. Math. Univ. Carolin., 1997, 38(3), 433–451 Google Scholar

[12] Gossez J.-P., Nonlinear elliptic boundary value problems for equations with rapidly (or slowly) increasing coefficients, Trans. Am. Math. Soc., 1974, 190, 163–205 http://dx.doi.org/10.1090/S0002-9947-1974-0342854-2CrossrefGoogle Scholar

[13] Gustavsson J., Peetre J., Interpolation of Orlicz spaces, Studia Math., 1977, 60(1), 33–59 Google Scholar

[14] Gutiérrez C.E., Wheeden R.L., Sobolev interpolation inequalities with weights, Trans. Amer. Math. Soc., 1991, 323(1), 263–281 Google Scholar

[15] Haroske D., Skrzypczak L., Entropy numbers of embeddings of function spaces with Muckenhoupt weights, III. Some limiting cases, J. Funct. Spaces Appl., 2011, 9(2), 129–178 http://dx.doi.org/10.1155/2011/928962Web of ScienceCrossrefGoogle Scholar

[16] Kałamajska A., Pietruska-Pałuba K., On a variant of the Hardy inequality between weighted Orlicz spaces, Studia Math., 2009, 193(1), 1–28 http://dx.doi.org/10.4064/sm193-1-1CrossrefGoogle Scholar

[17] Kałamajska A., Pietruska-Pałuba K., On a variant of the Gagliardo-Nirenberg inequality deduced from the Hardy inequality, Bull. Pol. Acad. Sci. Math., 2011, 59(2), 133–149 http://dx.doi.org/10.4064/ba59-2-4CrossrefGoogle Scholar

[18] Kałamajska A., Pietruska-Pałuba K., Weighted Hardy-type inequalities in Orlicz spaces, J. Inequal. Appl., 2012, 12(4), 745–766 Google Scholar

[19] Kokilashvili V., Krbec M., Weighted inequalities in Lorentz and Orlicz spaces, World Scientific, River Edge, 1991 Google Scholar

[20] Koskela P., Lehrbäck J., Weighted pointwise Hardy inequalities, J. Lond. Math. Soc., 2009, 79(3), 757–779 http://dx.doi.org/10.1112/jlms/jdp013CrossrefGoogle Scholar

[21] Krasnosel’kii M.A., Rutickii Ya.B., Convex Functions and Orlicz Spaces, Noordhoff, Groningen, 1961 Google Scholar

[22] Kufner A., Weighted Sobolev Spaces, John Wiley & Sons, New York, 1985 Google Scholar

[23] Kufner A., Maligranda L., Persson L.-E., The Hardy Inequality, Vydavatelský Servis, Plzeň, 2007 Google Scholar

[24] Kufner A., Persson L.-E., Weighted Inequalities of Hardy Type, World Scientific, River Edge, 2003 Google Scholar

[25] Lai Q., Weighted modular inequalities for Hardy type operators, Proc. London Math. Soc., 1999, 79(3), 649–672 http://dx.doi.org/10.1112/S0024611599012010CrossrefGoogle Scholar

[26] Mazýa V.G., Sobolev Spaces, Springer Ser. Soviet Math., Springer, Berlin, 1985 Google Scholar

[27] Mitronovic D.S., Pečaric J.E., Fink A.M., Classical and New Inequalities in Analysis, Math. Appl. (East European Ser.), 61, Kluwer, Dordrecht, 1993 Google Scholar

[28] Muckenhoupt B., Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc., 1972, 165, 207–226 http://dx.doi.org/10.1090/S0002-9947-1972-0293384-6CrossrefGoogle Scholar

[29] Oinarov R., On weighted norm inequalities with three weights, J. London Math. Soc., 1993, 48(1), 103–116 http://dx.doi.org/10.1112/jlms/s2-48.1.103CrossrefGoogle Scholar

[30] Oleszkiewicz K., Pietruska-Pałuba K., Orlicz-space Hardy and Landau-Kolmogorov inequalities for Gaussian measures, Demonstratio Math., 2012, 45(2), 227–241 Google Scholar

[31] Opic B., Kufner A., Hardy-Type Inequalities, Pitman Res. Notes Math. Ser., 219, Longman Scientific & Technical, Harlow, 1990 Google Scholar

[32] Pilarczyk D., Asymptotic stability of singular solution to nonlinear heat equation, Discrete Contin. Dyn. Syst., 2009, 25(3), 991–1001 http://dx.doi.org/10.3934/dcds.2009.25.991CrossrefGoogle Scholar

[33] Rao M.M., Ren Z.D., Theory of Orlicz Spaces, Monogr. Textbooks Pure Appl. Math., 146, Marcel Dekker, New York, 1991 Google Scholar

[34] Simonenko I.B., Interpolation and extrapolation of linear operators in Orlicz spaces, Mat. Sb., 1964, 63(105), 536–553 (in Russian) Google Scholar

[35] Vazquez J.L., Zuazua E., The Hardy inequality and the asymptotic behaviour of the heat equation with an inversesquare potential, J. Funct. Anal., 2000, 173(1), 103–153 http://dx.doi.org/10.1006/jfan.1999.3556CrossrefGoogle Scholar

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