Multiplicative Inequalities of Carlson Type and Interpolation

One-Dimensional Interpolation Inequalities, Carlson–Landau Inequalities, and Magnetic Schrödinger Operators

“…The Carlson inequality [3] has been a source of many improvements, refinements and generalizations (see [7], [12] and the references therein). The constant π here is sharp and the inequality is strict unless {a k } ∞ k=1 ≡ 0.…”

Lower Bounds for Possible Singular Solutions for the Navier–Stokes and Euler Equations Revisited

“…Now we pick r = 1 2 s − 1 2 , and apply the interpolation technique employed by Hardy in his proof of Carlson's inequality (see [6]), to the first factor on the right hand side of (3), to obtain: , if we choose a = u(t) 2 s+1 and b = u(t) 2 s then the energy inequality (3) becomes Therefore, from inequality (4) we obtain and q = 2 5 2 −s . We thus get…”

“…The proof of this result requires a detailed inspection of the bounds on the nonlinear term of the Navier-Stokes equations found in [11], and the application of an interpolation technique inspired by the method used by Hardy to prove Carlson's inequality (see [6]). We must add that this problem using different techniques has been treated in the papers [2] and [10].…”

Sharp interpolation inequalities for discrete operators and applications

“…This inequality has attracted a lot of interest and has been a source of generalizations and improvements (see, for example, [10,12] and the references therein, and also [18] for the most recent strengthening of (6.1)). Inequality (6.1) has an integral analog (with the same sharp constant)…”