An improvement of Hölder’s inequality with r-conjugate exponents
relative to Lp-norm
Abstract
This paper investigates the Hölder’s inequality under the condition
r-conjugate exponents in the sense that ∑1/p_k=1/r. Successively, we
have, under r-conjugate exponents relative to the Lp-norm, investigated
generalized Hölder’s inequality, the interpolation of Hölder’s
inequality, and generalized s-order Hölder’s inequality which is an
expansion of the known Hölder’s inequality.