Fabricant, Alexander; Kutev, Nikolai; Rangelov, Tsviatko Hardy-type inequality with double singular kernels. (English) Zbl 1281.26013 Cent. Eur. J. Math. 11, No. 9, 1689-1697 (2013). Summary: A Hardy-type inequality with singular kernels at zero and on the boundary \(\partial \Omega \) is proved. Sharpness of the inequality is obtained for \(\Omega = B _{1}(0)\). Cited in 4 Documents MSC: 26D10 Inequalities involving derivatives and differential and integral operators Keywords:Hardy inequality; sharp estimates PDFBibTeX XMLCite \textit{A. Fabricant} et al., Cent. Eur. J. Math. 11, No. 9, 1689--1697 (2013; Zbl 1281.26013) Full Text: DOI References: [1] Adimurthi, Chaudhuri N., Ramaswamy M., An improved Hardy-Sobolev inequality and its application, Proc. Amer. Math. Soc., 2002, 130(2), 489-505 http://dx.doi.org/10.1090/S0002-9939-01-06132-9; · Zbl 0987.35049 [2] Alvino A., Volpicelli R., Volzone B., On Hardy inequalities with a remainder term, Ric. Mat., 2010, 59(2), 265-280 http://dx.doi.org/10.1007/s11587-010-0086-5; · Zbl 1204.35079 [3] Brezis H., Marcus M., Hardy’s inequalities revisited, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 1997, 25(1-2), 217-237; · Zbl 1011.46027 [4] Brezis H., Vázquez J.L., Blow-up solutions of some nonlinear elliptic problems, Rev. Mat. Univ. Complut. Madrid, 1997, 10(2), 443-469; · Zbl 0894.35038 [5] Filippas S., Tertikas A., Optimizing improved Hardy inequalities, J. Funct. Anal., 2002, 192(1), 186-233 http://dx.doi.org/10.1006/jfan.2001.3900; · Zbl 1030.26018 [6] Ghoussoub N., Moradifam A., On the best possible remaining term in the Hardy inequality, Proc. Natl. Acad. Sci. USA, 2008, 105(37), 13746-13751 http://dx.doi.org/10.1073/pnas.0803703105; · Zbl 1205.26033 [7] Gradsteyn I.S., Ryzhik I.M., Table of Integrals, Series and Products, Academic Press, New York, 1980; [8] Maz’ja V.G., Sobolev Spaces, Springer Ser. Soviet Math., Springer, Berlin, 1985; [9] Nazarov A.I., Dirichlet and Neumann problems to critical Emden-Fowler type equations, J. Global. Optim., 2008, 40(1-3), 289-303 http://dx.doi.org/10.1007/s10898-007-9193-6; · Zbl 1295.49003 [10] Pinchover Y., Tintarev K., Existence of minimizers for Schrödinger operators under domain perturbations with application to Hardy’s inequality, Indiana Univ. Math. J., 2005, 54(4), 1061-1074 http://dx.doi.org/10.1512/iumj.2005.54.2705; · Zbl 1213.35216 [11] Shen Y., Chen Z., Sobolev-Hardy space with general weight, J. Math. Anal. Appl., 2006, 320(2), 675-690 http://dx.doi.org/10.1016/j.jmaa.2005.07.044; · Zbl 1121.46032 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.