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We establish L p and L p (l Q ) estimates for singular integral operators with variable operator-valued product kernels. Application to the strong maximal function, double Hilbert transform, Littlewood-Paley inequalities and Fourier multipliers for //-spaces with mixed norm are given.

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Given 0 < s ≤ 1 and à an s-convex function, s − à -sequence spaces are introduced. Several quasi-Banach sequence spaces are thus characterized as a particular case of s − Ã-spaces. For these spaces, new measures of noncompactness are also defi ned, related to the Hausdorff measure of noncompactness. As an application, compact sets in s − Ã-interpolation spaces of a quasi-Banach couple are studied.

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