Brezis–Marcus type inequalities with Lamb constant

Abstract

Hardy-type inequalities with an additional term are proved for compactly supported smooth functions on open convex sets in the Euclidean space. We obtain one-dimensional Lp-inequalities and their multidimensional analogs on arbitrary domains, on regular sets, on domains with θ-cone condition and on convex domains. We use Bessel's function and the Lamb constant.

Неравенства Харди С Дополнительными Слагаемыми И Уравнения Типа Лэмба

“…502]). Поэтому, следуя [8,9,[33][34][35][36], величину λ ν будем называть константой Лэмба, а уравнение (4) параметрическим уравнением Лэмба.…”

Hardy type inequalities and parametric Lamb equation

“…We refer to [6,22,26,31,32,33,34,35,36,40] for other interesting Hardy type inequalities with additional nonnegative terms. We pay attention only to the fact that Hardy inequalities with remainders were first obtained by V.G.…”