Vol. 103, No. 2, 1982

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Best possible results in a class of inequalities

Peter Dexter Johnson, Jr. and R. N. Mohapatra

Vol. 103 (1982), No. 2, 433–436
Abstract

In this paper we shall prove the following theorem.

Theorem. Suppose 1 < p , and rp > 1 if p < , r > 0 if p = . Suppose the matrix A = (ank) with ank = nr (k n), ank = 0 (k > n). Suppose w be the subset of w consisting of nonnegative, monotone sequences. Then {nr1}n is maximum, with respect to <, in I where

I = {b w :  for some K > 0,A|bx|∥p Kxp for all x lp}.

Mathematical Subject Classification 2000
Primary: 26D15
Secondary: 40C05
Milestones
Received: 28 July 1980
Published: 1 December 1982
Authors
Peter Dexter Johnson, Jr.
R. N. Mohapatra