Hölder-Young bounds for operators with regular kernels, Hardy-Littlewood bounds for operators with weakly singular kernels, and Calderon- Zygmund bounds for strongly singular convolution operators over Euclidean space
نویسنده
چکیده
It easy to see that every bounded linear operator is continuous. It is not hard to show that the converse is also true. The notions of bounded and continuous thereby coincide for linear operators acting between normed spaces. It is customary to prefer the terminology bounded linear operator over that of continuous linear operator. The reason for this preference is the fact that the hard part of showing a linear operator is continuous is usually establishing the bound (1.2).
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