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1
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Homotonic algebras

100%
Cwikel M., Goldberg M.
Studia Mathematica
|
2009
|
tom 195
|
nr 3
287-295
EN
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.
2
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Interpolation on families of characteristic functions

100%
Cwikel M., Gulisashvili A.
Studia Mathematica
|
2000
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tom 138
|
nr 3
209-224
EN
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 $\overline Φ =(B,L^∞)$ 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 $(B,L^∞)_{θ,p}$ in terms of the characteristic functions of the level sets of ⨍.
3
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A geometrical/combinatorical question with implications for the John-Nirenberg inequality for BMO functions

81%
Cwikel M., Sagher Y., Shvartsman P.
Banach Center Publications
|
2011
|
tom 95
|
nr 1
45-53
EN
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 celebrated John-Nirenberg inequality and of related inequalities due to John and to Wik. One of our main results is that an affirmative answer to the above question would lead to a version of the John-Nirenberg inequality with "dimension free" constants.
4
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Interpolation of analytic families of operators

50%
Cwikel M., Janson S.
Studia Mathematica
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1984
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tom 79
|
nr 1
61-71
5
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The canonical seminorm on Weak L¹

50%
Cwikel M., Fefferman C.
Studia Mathematica
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1984
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tom 78
|
nr 3
275-278
6
Content available remote

On the conjugates of some function spaces

50%
Cwikel M.
Studia Mathematica
|
1973
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tom 45
|
nr 1
49-55
7
Content available remote

Maximal seminorms on Weak $L^{1}$

40%
Cwikel M., Fefferman C.
Studia Mathematica
|
1981
|
tom 69
|
nr 2
149-154
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