On the Support of the Measures in a Symmetric Convolution Semigroup.
On the supports and absolute continuity of infinitely divisible probability measures.
On the Symmetry of Generalized L1-Algebras.
On the Symplectic Structure of Coadjoint Orbits of (Solvable) Lie Groups and Applications. I.
On the theorem of F. and M. Riesz
On the traces of W2,p(Ω) for a Lipschitz domain.
We extend to the case 1 < p the results obtained by Geymonat and Krasucki for p = 2 on the characterization of the traces of W2,p(Ω) for a bounded Lipschitz domain.
On the uniqueness of uniform norms and C*-norms
We prove that a semisimple, commutative Banach algebra has either exactly one uniform norm or infinitely many uniform norms; this answers a question asked by S. J. Bhatt and H. V. Dedania [Studia Math. 160 (2004)]. A similar result is proved for C*-norms on *-semisimple, commutative Banach *-algebras. These properties are preserved if the identity is adjoined. We also show that a commutative Beurling *-algebra L¹(G,ω) has exactly one uniform norm if and only if it has exactly one C*-norm; this is...
On the vector-valued Fourier transform and compatibility of operators
Let be a locally compact abelian group and let 1 < p ≤ 2. ’ is the dual group of , and p’ the conjugate exponent of p. An operator T between Banach spaces X and Y is said to be compatible with the Fourier transform if admits a continuous extension . Let denote the collection of such T’s. We show that for any and positive integer n. Moreover, if the factor group of by its identity component is a direct sum of a torsion-free group and a finite group with discrete topology then .
On the Wiener-Eberlein theorem
On Transformation of Exceptional sets
On trigonometric polynomials spanned by characters of unitary representations.
On ultra-weak convergence in
On unicity of the Riesz decomposition of an excessive measure.
On uniqueness of G-measures and g-measures
We give a simple proof of the sufficiency of a log-lipschitzian condition for the uniqueness of G-measures and g-measures which were studied by G. Brown, A. H. Dooley and M. Keane. In the opposite direction, we show that the lipschitzian condition together with positivity is not sufficient. In the special case where the defining function depends only upon two coordinates, we find a necessary and sufficient condition. The special case of Riesz products is discussed and the Hausdorff dimension of...
On unitary representations of Jacobi groups.
On vector-valued Hardy martingales and a generalized Jensen's inequality.
On vector-valued inequalities for Sidon sets and sets of interpolation
Let E be a Sidon subset of the integers and suppose X is a Banach space. Then Pisier has shown that E-spectral polynomials with values in X behave like Rademacher sums with respect to -norms. We consider the situation when X is a quasi-Banach space. For general quasi-Banach spaces we show that a similar result holds if and only if E is a set of interpolation (-set). However, for certain special classes of quasi-Banach spaces we are able to prove such a result for larger sets. Thus if X is restricted...
On weighted inequalities for operators of potential type
In this paper, we discuss a class of weighted inequalities for operators of potential type on homogeneous spaces. We give sufficient conditions for the weak and strong type weighted inequalities sup_{λ>0} λ|{x ∈ X : |T(fdσ)(x)|>λ }|_{ω}^{1/q} ≤ C (∫_{X} |f|^{p}dσ)^{1/p} and (∫_{X} |T(fdσ)|^{q}dω )^{1/q} ≤ C (∫_X |f|^{p}dσ )^{1/p} in the cases of 0 < q < p ≤ ∞ and 1 ≤ q < p < ∞, respectively, where T is an operator of potential type, and ω and σ are Borel measures on the homogeneous...
On Weyl Operators over Locally Compact Abelian Groups.
On φ-inner amenable Banach algebras
Generalizing the concept of inner amenability for Lau algebras, we define and study the notion of φ-inner amenability of any Banach algebra A, where φ is a homomorphism from A onto ℂ. Several characterizations of φ-inner amenable Banach algebras are given.