On the conjugates of some function spaces
The dual of weak
For , a characterization is given of the dual space of weak taken over a non atomic measure space.
Sobolev Type Embeddings in the Limiting Case.
A new characterization of the interpolation spaces between L... and L...
Interpolation of Marcinkiewicz spaces.
Maximal seminorms on Weak
The canonical seminorm on Weak L¹
Interpolation on families of characteristic functions
We study a problem of interpolating a linear operator which is bounded on some family of characteristic functions. A new example is given of a Banach couple of function spaces for which such interpolation is possible. This couple is of the form where B is an arbitrary Banach lattice of measurable functions on a σ-finite nonatomic measure space (Ω,Σ,μ). We also give an equivalent expression for the norm of a function ⨍ in the real interpolation space in terms of the characteristic functions of...
Interpolation of analytic families of operators
Homotonic algebras
An algebra 𝓐 of real- or complex-valued functions defined on a set T shall be called homotonic if 𝓐 is closed under taking absolute values, and for all f and g in 𝓐, the product f × g satisfies |f × g| ≤ |f| × |g|. Our main purpose in this paper is two-fold: to show that the above definition is equivalent to an earlier definition of homotonicity, and to provide a simple inequality which characterizes submultiplicativity and strong stability for weighted sup norms on homotonic algebras.
A geometrical/combinatorical question with implications for the John-Nirenberg inequality for BMO functions
The first and last sections of this paper are intended for a general mathematical audience. In addition to some very brief remarks of a somewhat historical nature, we pose a rather simply formulated question in the realm of (discrete) geometry. This question has arisen in connection with a recently developed approach for studying various versions of the function space BMO. We describe that approach and the results that it gives. Special cases of one of our results give alternative proofs of the...
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