It is proved that the reiteration theorem is not valid for the spaces Ap (theta,q) defined by V. Popov by means of onesided approximation. It is also proved that a class of cones, defined by onesided approximation of piecewise linear functions on the interval [0,1], is stable for the real interpolation method.
We prove an interpolation theorem for weak-type operators. This is closely related to interpolation between weak-type classes. Weak-type classes at the ends of interpolation scales play a similar role to that played by BMO with respect to the interpolation scale. We also clarify the roles of some of the parameters appearing in the definition of the weak-type classes. The interpolation theorem follows from a K-functional inequality for the operators, involving the Calderón operator. The inequality...
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