Interpolation of operators

@inproceedings{Bennett1987InterpolationOO,
  title={Interpolation of operators},
  author={Colin Bennett and Mark S. Sharpley},
  year={1987}
}

Interpolation between Banach spaces and continuity of Radon-like integral transforms

We present the abstract framework and some applications of interpolation theory. The main new result concerns interpolation between H^1 and L^p estimates for analytic families of operators acting on

On the Hardy-type integral operators in Banach function spaces

Characterization of the mapping properties such as boundedness, compactness, measure of non-compactness and estimates of the approximation numbers of Hardy-type integral operators in Banach function

Matrix multiplication operators on Banach function spaces

In this paper, we study the matrix multiplication operators on Banach function spaces and discuss their applications in semigroups for solving the abstract Cauchy problem.

Optimality of Function Spaces in Sobolev Embeddings

Abstract We study the optimality of function spaces that appear in Sobolev embeddings. We focus on rearrangement-invariant Banach function spaces. We apply methods of interpolation theory.

Multiplication Semigroups on Banach Function Spaces

In this paper we characterize multiplication operators induced by operator valued maps on Banach function spaces. We also study multiplication semigroups and stability of these operators.

Interpolation of linear operators

The survey is devoted to the modern state of the theory of interpolation of linear operators acting in Banach spaces. Principal attention is devoted to real and complex methods and applications of

Interpolation of compact bilinear operators among quasi‐Banach spaces and applications

We study the interpolation properties of compact bilinear operators by the general real method among quasi‐Banach couples. As an application we show that commutators of Calderón–Zygmund bilinear

Banach envelopes of holomorphic Hardy spaces

We identify the Banach envelope of Hardy type spaces Hp, p < 1, of holomorphic functions in Lipschitz domains in the form of suitable Bergman type spaces of analytic functions.

Interpolation of Classical Lorentz Spaces1

We describe the K-functional and identify the real interpolated spaces of general quasi–Banach couples of classical Lorentz spaces. Applications are given which include interpolation of spaces of

LOGARITHMIC INTERPOLATION METHODS AND MEASURE OF NON-COMPACTNESS

We derive interpolation formulae for the measure of non-compactness of operators interpolated by logarithmic methods with [θ] = 0; 1 between quasi-Banach spaces. Applications are given to operators
...

References

Three classical interpolation theorems form the foundation of the modern theory of interpolation of operators. They are the M. Riesz convexity theorem

  • 1939