Takahashi, Futoshi A simple proof of Hardy’s inequality in a limiting case. (English) Zbl 1308.35010 Arch. Math. 104, No. 1, 77-82 (2015). Summary: We provide a simple proof of Hardy’s inequality in a limiting case. In the proof we do not need any symmetrization technique such as the Polya-Szegő inequality for the spherical decreasing rearrangement. Cited in 26 Documents MSC: 35A23 Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals 26D15 Inequalities for sums, series and integrals 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems Keywords:Hardy’s inequality; limiting case; spherical decreasing rearrangement PDFBibTeX XMLCite \textit{F. Takahashi}, Arch. Math. 104, No. 1, 77--82 (2015; Zbl 1308.35010) Full Text: DOI Link References: [1] Adimurthi N.C., Ramaswamy M.: An improved Hardy-Sobolev inequality and its application, Proc. Amer. Math. Soc., 130, 489-505 (2001) · Zbl 0987.35049 · doi:10.1090/S0002-9939-01-06132-9 [2] Adimurthi and K. Sandeep, Existence and non-existence of the first eigenvalue of the perturbed Hardy-Sobolev operator, Proc. Roy. Soc. Edinburgh Sect. A, 132, 1021-1043 (2002) · Zbl 1029.35194 [3] García Azorero J.P., Peral Alonso I.: Hardy inequalities and some critical elliptic and parabolic problems. J. Differential Equations. 144, 441-476 (1998) · Zbl 0918.35052 · doi:10.1006/jdeq.1997.3375 [4] Costa D.G.: Some new and short proofs for a class of Caffarelli-Kohn-Nirenberg type inequalities. J. Math. Anal. Appl., 337, 311-317 (2008) · Zbl 1127.26017 · doi:10.1016/j.jmaa.2007.03.062 [5] Y. Di, L. Jiang, S. Shen, and Y. Jin, A note on a class of Hardy-Rellich type inequalities, J. Inequal. Appl., 2013:84 (2013), 1-6 · Zbl 1284.26030 [6] Ioku N.: Sharp Sobolev inequalities in Lorenz spaces for a mean oscillation. J. Funct. Anal., 266, 2914-2958 (2014) · Zbl 1312.46039 · doi:10.1016/j.jfa.2013.12.023 [7] N. Ioku and M. Ishiwata, A scale invariant form of a critical Hardy inequality, Int. Math. Res. Not. IMRN, to appear, doi:10.1093/imrn/rnu212, 17 pages · Zbl 1326.26035 [8] O.A. Ladyzhenskaya, The mathematical theory of viscous incompressible flow, Second edition, revised and enlarged. Mathematics and its Applications, Vol. 2 Gordon and Breach, Science Publishers, New York-London-Peris, (1969) · Zbl 0184.52603 [9] Machihara S., Ozawa T., Wadade H.: Hardy type inequalities on balls. Tohoku Math. J. (2) 65, 321-330 (2013) · Zbl 1281.26015 · doi:10.2748/tmj/1378991018 [10] Mitidieri E.: A simple approach to Hardy inequalities. Mathematical Notes,. 67, 563-572 (2000) · Zbl 0964.26010 · doi:10.1007/BF02676404 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.