In telescopic homotopy theory, a space or spectrum X is approximated by a tower of localizations LnX, n ≥ 0, taking account of vn-periodic homotopy groups for progressively higher n. For each n ≥ 1, we construct a telescopic Kuhn functor Φn carrying a space to a spectrum with the same vn-periodic homotopy groups, and we construct a new functor Θn left adjoint to Φn. Using these functors, we sho...

In this paper, we prove the existence of solutions of initial value problems for nth order nonlinear impulsive integro-differential equations of mixed type on an infinite interval with an infinite number of impulsive times in Banach spaces. Our results are obtained by introducing a suitable measure of noncompactness.

We introduce weighted amalgam-type spaces and analyze their relations with some known spaces. Integrability results for the Fourier transform of a function derivative from one those are proved. The obtained applied to integrability trigonometric series sequence coefficients bounded variation.

We define a Muckenhoup-type condition on weighted Morrey spaces using the Köthe dual of space. show that is necessary and sufficient for boundedness maximal operator defined with balls centered at origin spaces. A modified characterizes inequalities Calderón operator. also local usual Hardy–Littlewood operator, simplifying previous characterization Nakamura–Sawano–Tanaka. For same in case globa...

The boundedness and compactness of the weighted composition operator from weighted Hardy spaces to weighted-type spaces are studied in this paper.