For every symmetric quasi-Banach space inside the Lorentz space Λ log, the paper constructs and proves optimal (smallest) symmetric quasi-Banach range spaces for the Calderón operator, the Hilbert transform, and the triangular truncation operator.
Arazy, Some remarks on interpolation theorems and the boundedness of the triangular projection in unitary matrix spaces , Integr
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The optimal range of the Calder\`{o}n operator and its applications
For every symmetric quasi-Banach space inside the Lorentz space Λ log, the paper constructs and proves optimal (smallest) symmetric quasi-Banach range spaces for the Calderón operator, the Hilbert transform, and the triangular truncation operator.