This work is solely dedicated to the study of both the one variable as well as the multidimensional Lorentz spaces covering the theory of Lebesgue type spaces invariant by rearrangement. The authors provide proofs in full detail for most theorems. The self-contained text is valu…
"The Cambridge Monographs on Applied and Computational Mathematics series reflects the crucial role of mathematical and computational techniques in contemporary science. The series publishes expositions on all aspects of applicable and numerical mathematics, with an emphasis on …
"The Cambridge Monographs on Applied and Computational Mathematics series reflects the crucial role of mathematical and computational techniques in contemporary science. The series publishes expositions on all aspects of applicable and numerical mathematics, with an emphasis on …
Quasi-interpolation is one of the most useful and often applied methods for the approximation of functions and data in mathematics and applications. Its advantages are manifold: quasi-interpolants are able to approximate in any number of dimensions, they are efficient and relati…
Quasi-interpolation is one of the most useful and often applied methods for the approximation of functions and data in mathematics and applications. Its advantages are manifold: quasi-interpolants are able to approximate in any number of dimensions, they are efficient and relati…
Recently, Jawerth, Rochberg and Weiss have studied nonlinear maps arising from interpolation theory which satisfy commutator relationships with interpolated linear operators. Here we present a very general result of this type for rearrangement-invariant Banach function spaces.
We develop a general theory of extrapolation spaces, a complement to the familiar theory of interpolation spaces. Our results allow us to extend the classical extrapolation theorem of Yano to scales of Banach spaces. We give applications to classical and modern analysis includin…
