Abstract

In this article we interpolate Young’s inequality using a delicate treatment of dyadics. Although there are other simple methods to prove these results, we present this new approach hoping to reveal more of the hidden properties of such inequalities.

Highlights

  • Young’s inequality for real numbers states that, for a, b ∈ R+ and p, q > satisfying 1 p + 1 q = 1, we have ab

  • In this work we tackle the problem in a different approach, where we introduce infinitely many Young-type inequalities, among which the known Young inequality is the weakest

  • We shall present our proofs in terms of what we defined as a ring-pair and a norm-mean mapping

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Summary

Introduction

We can use inequality (1.3) to obtain the following interpolated version, whose simple proof appeared in [8]. ApXBq ≤ p Ap+qX + q XBp+q p+q p+q for any unitarily invariant norm | | on Mn. This inequality was first proved in [1]. We shall present our proofs in terms of what we defined as a ring-pair and a norm-mean mapping.

Results
Conclusion
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