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An interpolation theorem related to the a.e. convergence of integral operators.
ABSTRACT. We show that for integral operators of general form the norm bounds in Lorentz spaces imply certain norm bounds for the maximal function. As a consequence, the a.e. convergence for the integral operators on the Lorentz spaces follows from the appropriate
norm estimates. Applications to the spectral theory of one-dimensional Schr\"odinger operators are discussed.