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Hardy type inequalities in L p with sharp remainders

Sharp remainder terms are explicitly given on the standard Hardy inequalities in L p ( R n ) with 1 < p < n . Those remainder terms provide a direct and exact understanding of Hardy type inequalities in the framework of equalities as well as of the nonexistence of nontrivial extremals. MSC: 26D10, 26D15, 46E35.

Scaling invariant Hardy inequalities of multiple logarithmic type on the whole space

In this paper, we establish Hardy inequalities of logarithmic type involving singularities on spheres in R n in terms of the Sobolev-Lorentz-Zygmund spaces. We prove it by absorbing singularities of functions on the spheres by subtracting the corresponding limiting values. MSC: 46E35, 26D10.

Stability of the Young and Hölder inequalities

We give a simple proof of the Aldaz stability version of the Young and Hölder inequalities and further refinements of available stability versions of those inequalities.MSC: 26D15.

Generalizations of the logarithmic Hardy inequality in critical Sobolev-Lorentz spaces

In this paper, we establish the Hardy inequality of the logarithmic type in the critical Sobolev-Lorentz spaces. More precisely, we generalize the Hardy type inequality obtained in Edmunds and Triebel (Math. Nachr. 207:79-92, 1999). The generalized inequality allows us to take the exponents appearing in the inequality more flexibly, and its optimality is discussed in detail. O...

Regularity Criterion for Weak Solutions to the Navier-Stokes Equations in Terms of the Gradient of the Pressure

Tohru Ozawa 0 0 Department of Applied Physics, Waseda University , Tokyo 169-8555 , Japan 1 Department of Applied Mathematics, Nanjing Forestry University , Nanjing 210037 , China We prove a regularity

Remarks on modified improved Boussinesq equations in one space dimension

We study the existence and scattering of global small amplitude solutions to modified improved Boussinesq equations in one dimension with nonlinear term behaving as a power as . Solutions are considered in space for all . According to the value of s, the power nonlinearity exponent p is determined. Liu (Liu 1996 Indiana Univ. Math. J. 45, 797–816) obtained the minimum value of p...