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For a fixed sequence f. = (fn ) of independent identically distributed symmetric random variables with , we introduce the notion of Kf. -convex Banach space and the notions of (fn )-bounding and (fn )-converging operators acting between Banach spaces. It is shown that the dual of the space of (fn )-converging operators between a Hilbert space and a Kf. -convex Banach space admits a precise description in terms of trace duality. The obtained results recover similar formulations for almost summing and γ-Radonifying operators.

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Abstract. We show decay bounds of the formfor integrable and bounded solutions to the nonlocal evolution equationHere G is a nonnegative and even function and f verifies f (ξ)ξ ≤ 0 for all ξ ≥ 0. We remark that G is not assumed to be homogeneous. The function φ and the exponent µ depend on G via adequate hypotheses, while J is a nonnegative kernel satisfying suitable assumptions.

No abstract