This paper establishes tight upper and lower bounds on Lipschitz aggregation operators considering their diagonal, opposite diagonal and marginal sections. Also we provide explicit formulae to determine the bounds. These are useful for construction of these type of aggregation operators, especially using interpolation schemata.

We develop a framework that enables us to study a broad class of special values of the Katz two-variable p-adic L-functions, including certain special values lying outside the range of p-adic interpolation.

Introduction Conclusions References

Proposition 2. A is restricted weak-type (pd, qd). Proof (Proposition 2 ⇒ Theorem 1). Proposition 2 corresponds to an estimate at the vertex Pd of the trapezium. Since A and the adjoint operator A ∗ have the same mapping properties, one concludes there is a restricted weak-type estimate for the exponents corresponding to the vertex P ′ d. By localisation we know A is type (1, 1) and type (∞,∞) ...

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Let M be a semifinite von Neumann algebra equipped with a semifinite normal faithful trace τ . Let d be an injective positive measurable operator with respect to (M, τ ) such that d is also measurable. Define Lp(d) = {x ∈ L0(M) : dx+ xd ∈ Lp(M)} and ‖x‖Lp(d) = ‖dx+ xd‖p . We show that for 1 6 p0 < p1 6 ∞, 0 < θ < 1 and α0 > 0, α1 > 0 the interpolation equality (Lp0(d 0), Lp1(d α))θ = Lp(d ) hol...

We prove uniform estimates for the expected value of averages of order statistics of matrices in terms of their largest entries. As an application, we obtain similar probabilistic estimates for `p norms via real interpolation.

We define abstract derivations for equational logic and use them to prove the interpolation property.