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Concentration-Compactness Principle for embedding into multiple exponential spaces on unbounded domains

Robert Černý (2015)

Czechoslovak Mathematical Journal

Let Ω ⊂ ℝ n be a domain and let α < n - 1 . We prove the Concentration-Compactness Principle for the embedding of the space W 0 1 L n log α L ( Ω ) into an Orlicz space corresponding to a Young function which behaves like exp ( t n / ( n - 1 - α ) ) for large t . We also give the result for the embedding into multiple exponential spaces. Our main result is Theorem where we show that if one passes to unbounded domains, then, after the usual modification of the integrand in the Moser functional, the statement of the Concentration-Compactnes Principle is very...

Concerning entire functions in B 0 -algebras

W. Żelazko (1994)

Studia Mathematica

We construct a non-m-convex non-commutative B 0 -algebra on which all entire functions operate. Our example is also a Q-algebra and a radical algebra. It follows that some results true in the commutative case fail in general.

Concerning weak * -extreme points

Eva Matoušková (1995)

Commentationes Mathematicae Universitatis Carolinae

Every separable nonreflexive Banach space admits an equivalent norm such that the set of the weak * -extreme points of the unit ball is discrete.

Conditional Fourier-Feynman transform given infinite dimensional conditioning function on abstract Wiener space

Jae Gil Choi, Sang Kil Shim (2023)

Czechoslovak Mathematical Journal

We study a conditional Fourier-Feynman transform (CFFT) of functionals on an abstract Wiener space ( H , B , ν ) . An infinite dimensional conditioning function is used to define the CFFT. To do this, we first present a short survey of the conditional Wiener integral concerning the topic of this paper. We then establish evaluation formulas for the conditional Wiener integral on the abstract Wiener space B . Using the evaluation formula, we next provide explicit formulas for CFFTs of functionals in the Kallianpur...

Conditionality constants of quasi-greedy bases in super-reflexive Banach spaces

F. Albiac, J. L. Ansorena, G. Garrigós, E. Hernández, M. Raja (2015)

Studia Mathematica

We show that in a super-reflexive Banach space, the conditionality constants k N ( ℬ ) of a quasi-greedy basis ℬ grow at most like O ( ( l o g N ) 1 - ε ) for some 0 < ε < 1. This extends results by the third-named author and Wojtaszczyk (2014), where this property was shown for quasi-greedy bases in L p for 1 < p < ∞. We also give an example of a quasi-greedy basis ℬ in a reflexive Banach space with k N ( ℬ ) ≈ l o g N .

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