Hardy type inequalities with spherical derivatives

Beckner, W.: Pitt’s inequality and the fractional Laplacian: sharp error estimates. Forum Math. 24, 177–209 (2012)

Beckner, W.: Pitt’s inequality and the uncertainty principle. Proc. Am. Math. Soc. 123, 1897–1905 (1995)

Beckner, W.: Pitt’s inequality with sharp convolution estimates. Proc. Am. Math. Soc. 136, 1871–1885 (2008)

Bez, N., Jeavons, C., Ozawa, T., Sugimoto, M.: Stability of trace theorems on the sphere. J. Geom. Anal. 28, 1456–1476 (2018)

Bez, N., Machihara, S., Sugimoto, M.: Extremisers for the trace theorem on the sphere. Math. Res. Lett. 23, 633–647 (2016)

Bez, N., Saito, H., Sugimoto, M.: Applications of the Funk-Hecke theorem to smoothing and trace estimates. Adv. Math. 285, 1767–1795 (2015)

Birman, MSh, Laptev, A.: The negative discrete spectrum of a two-dimensional Schrödinger operator. Commun. Pure Appl. Math. 49, 967–997 (1996)

Bogdan, K., Dyda, B., Kim, P.: Hardy inequalities and non-explosion results for semigroups. Potential Anal. 44, 229–247 (2016)

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)

Davies, E.B., Hinz, A.M.: Explicit constants for Rellich inequalities in $$L^p(\Omega )$$. Math. Z. 227, 511–523 (1998)

Dolbeault, J., Volzone, B.: Improved Poincaré inequalities. Nonlinear Anal. 75, 5985–6001 (2012)

Ekholm, T., Frank, R.L.: On Lieb-Thirring inequalities for Schrödinger operators with virtual level. Commun. Math. Phys. 264, 725–740 (2006)

Ghoussoub, N., Moradifam, A.: Bessel pairs and optimal Hardy and Hardy–Rellich inequalities. Math. Ann. 349, 1–57 (2011)

Ghoussoub, N., Moradifam, A.: On the best possible remaining term in the Hardy inequality. Proc. Natl. Acad. Sci. USA 1305, 13746–13751 (2008)

Ioku, N., Ishiwata, M., Ozawa, T.: Sharp remainder of a critical Hardy inequality. Arch. Math. (Basel) 1, 65–71 (2016)

Ioku, N., Ishiwata, M., Ozawa, T.: Hardy type inequalities in $$L^p$$ with sharp remainders. J. Inequal. Appl. Paper No. 5 (2017)

Ioku, N., Ishiwata, M.: A scale invariant form of a critical Hardy inequality. Int. Math. Res. Not. IMRN 18, 8830–8846 (2015)

Lieb, E.H.: Sharp constants in the Hardy–Littlewood–Sobolev and related inequalities. Ann. Math. 118, 349–374 (1983)

Machihara, S., Ozawa, T., Wadade, H.: Hardy type inequalities on balls. Tohoku Math. J. 65, 321–330 (2013)

Machihara, S., Ozawa, T., Wadade, H.: Remarks on the Rellich inequality. Math. Z. 286, 1367–1373 (2017)

Machihara, S., Ozawa, T., Wadade, H.: Remarks on the Hardy type inequalities with remainder terms in the framework of equalities. Adv. Stud. Pure Math. 81, 247–258 (2016)

Ruzhansky, M., Suragan, D.: Hardy and Rellich inequalities, identities, and sharp remainders on homogeneous groups. Adv. Math. 317, 799–822 (2017)

Sano, M., Takahashi, F.: Scale invariance structures of the critical and the subcritical Hardy inequalities and their improvements. Calc. Var. Partial Differ. Equ. 56, 56–69 (2017)

Stein, E.M., Weiss, G.: Introduction to Fourier Analysis on Euclidean Spaces. Princeton Mathematical Series, No. 32, Princeton University Press, Princeton, N.J. (1971)

Takahashi, F.: A simple proof of Hardy’s inequality in a limiting case. Arch. Math. (Basel) 104, 77–82 (2015)

Walther, B.: Regularity, decay, and best constants for dispersive equations. J. Funct. Anal. 189, 325–335 (2002)

Yafaev, D.: Sharp constants in the Hardy-Rellich inequalities. J. Funct. Anal. 168, 121–144 (1999)