Hardy-type inequalities for matrix operators

Abstract

Hardy-type inequalities for matrix operatorsWe establish necessary and sufficient conditions the validity of the discrete Hardy-type inequalitywhere the matrices (ai,j) is an arbitrary matrix and the entries of the matrix (ai,j) ≥ 0 such that ai,j is non-increasing in the second index. Also some further results are pointed out on the cone of monotone sequences. Moreover, we give that the applications of the main results for the non-negative and triangular matrices (ai,j ≥ 0 for 1 ≤ j ≤ i and ai,j = 0 for i < j).

NEWTON'S TYPE QUANTUM FRACTIONAL INTEGRAL INEQUALITIES PERTAINING TO n-POLYNOMIAL CONVEX FUNCTIONS AND APPLICATION

“…(2.6) Theorem 3. (q-Hölder's inequality) [35] Let h1 , h2 be two q-integrable functions on [ χ 1 , χ 2 ], such that p, q * > 1 and 1 p + 1 q * = 1. Then we have…”