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Embedding theorems for Müntz spaces

Isabelle Chalendar, Emmanuel Fricain, Dan Timotin (2011)

Annales de l’institut Fourier

We discuss boundedness and compactness properties of the embedding M Λ 1 L 1 ( μ ) , where M Λ 1 is the closed linear span of the monomials x λ n in L 1 ( [ 0 , 1 ] ) and μ is a finite positive Borel measure on the interval [ 0 , 1 ] . In particular, we introduce a class of “sublinear” measures and provide a rather complete solution of the embedding problem for the class of quasilacunary sequences Λ . Finally, we show how one can recapture some of Al Alam’s results on boundedness and the essential norm of weighted composition operators from M Λ 1 ...

Essential norms of the Neumann operator of the arithmetical mean

Josef Král, Dagmar Medková (2001)

Mathematica Bohemica

Let K m ( m 2 ) be a compact set; assume that each ball centered on the boundary B of K meets K in a set of positive Lebesgue measure. Let C 0 ( 1 ) be the class of all continuously differentiable real-valued functions with compact support in m and denote by σ m the area of the unit sphere in m . With each ϕ C 0 ( 1 ) we associate the function W K ϕ ( z ) = 1 σ m m K g r a d ϕ ( x ) · z - x | z - x | m x of the variable z K (which is continuous in K and harmonic in K B ). W K ϕ depends only on the restriction ϕ | B of ϕ to the boundary B of K . This gives rise to a linear operator W K acting from...

Extreme points of the complex binary trilinear ball

Fernando Cobos, Thomas Kühn, Jaak Peetre (2000)

Studia Mathematica

We characterize all the extreme points of the unit ball in the space of trilinear forms on the Hilbert space 2 . This answers a question posed by R. Grząślewicz and K. John [7], who solved the corresponding problem for the real Hilbert space 2 . As an application we determine the best constant in the inequality between the Hilbert-Schmidt norm and the norm of trilinear forms.

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