Abstract
We prove a multiplicative inequality for inner products, which enables us to deduce improvements of inequalities of the Carlson type for complex functions and sequences, and also other known inequalities.
Highlights
Let an∞ n be a nonzero sequence of nonnegative numbers and let f be a measurable function on 0, ∞
W12 x f 2 x dx w22 x f 2 x dx Journal of Inequalities and Applications are known for special weight functions w1 and w2, where usually w1 and w2 are power functions or homogeneous
We prove a refined version of 1.3 for a fairly general class of weight functions see Corollary 3.2
Summary
∞ n be a nonzero sequence of nonnegative numbers and let f be a measurable function on 0, ∞. We prove a refined version of 1.3 for a fairly general class of weight functions see Corollary 3.2. This inequality shows that 1.2 holds with the constant π2 for many infinite weights beside the classical ones w1 x 1 and w2 x x. The paper is organized as follows: in Section 2 we prove our general multiplicative inequality for inner products.
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