A. P. Calderón

On an inverse boundary value problem

This paper is a reprint of the original work by A. P. Calderon published by the Brazilian Mathematical Society (SBM) in ATAS of SBM (Rio de Janeiro), pp. 65-73, 1980. The original paper had no abstract, so this reprint to be truthful to the original work is published with no abstract.

On the existence of certain singular integrals

Let f (x) and K (x) be two functions integrable over the interval (-∞,+∞). It is very well known that their composition

An atomic decomposition of distributions in parabolic Hp spaces

\int\limits_{{ - \infty }}^{{ + \infty }} {f(t)K\left( {x - t} \right)dt}

A General Ergodic Theorem

exists, as an absolutely convergent integral, for almost every x. The integral can, however, exist almost everywhere even if K is not absolutely integrable. The mostinteresting special case is that of K (x) = 1/x. Let us set

A note on singular integrals

\tilde{f}(x) = \frac{1}{\pi }\int\limits_{{ - \infty }}^{{ + \infty }} {\frac{{f(t)}}{{x - t}}dt}

CONVOLUTION OPERATORS ON BANACH SPACE VALUED FUNCTIONS.

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