The property of weak type (p,p) for the Hardy-Littlewood maximal operator and derivation of integrals
The property () of Orlicz-Bochner sequence spaces
A characterization of property of an arbitrary Banach space is given. Next it is proved that the Orlicz-Bochner sequence space has the property if and only if both spaces and have it also. In particular the Lebesgue-Bochner sequence space has the property iff has the property . As a corollary we also obtain a theorem proved directly in [5] which states that in Orlicz sequence spaces equipped with the Luxemburg norm the property , nearly uniform convexity, the drop property and...
The Radon measures as functionals on Lipschitz functions
The range of a contractive projection in Lp(H).
We show that the range of a contractive projection on a Lebesgue-Bochner space of Hilbert valued functions Lp(H) is isometric to a lp-direct sum of Hilbert-valued Lp-spaces. We explicit the structure of contractive projections. As a consequence for every 1 < p < ∞ the class Cp of lp-direct sums of Hilbert-valued Lp-spaces is axiomatizable (in the class of all Banach spaces).
The range of vector measures into Orlicz spaces
The range of vector valued holomorphic mappings
The regularity of the positive part of functions in with applications to parabolic equations
Let with be given. Then we show by means of a counter-example that the positive part of has less regularity, in particular it holds in general. Nevertheless, satisfies an integration-by-parts formula, which can be used to prove non-negativity of weak solutions of parabolic equations.
The role of Onofri type inequalities in the symmetry properties of extremals for Caffarelli-Kohn-Nirenberg inequalities, in two space dimensions
We first discuss a class of inequalities of Onofri type depending on a parameter, in the two-dimensional Euclidean space. The inequality holds for radial functions if the parameter is larger than . Without symmetry assumption, it holds if and only if the parameter is in the interval . The inequality gives us some insight on the symmetry breaking phenomenon for the extremal functions of the Caffarelli-Kohn-Nirenberg inequality, in two space dimensions. In fact, for suitable sets of parameters (asymptotically...
The S...-criterion for Hankel forms on the Fock space, 0 < p < 1.
The semi- property for normed Riesz spaces
The sharp Sobolev inequality in quantitative form
The singular set of the minima of certain quadratic functionals
The Sobolev capacity on metric spaces.
The Sobolev embeddings are usually sharp.
The Sobolev spaces of harmonic functions
The Sobolev-Besov imbedding theorem from the viewpoint of semi-groups of operators
The Sobolev-Il'in theorem for the -Riesz potential.
The space of countably simple bounded functions with values in a DF-space.
The Space of Differences of Convex Functions on [0, 1]
∗Participant in Workshop in Linear Analysis and Probability, Texas A & M University, College Station, Texas, 2000. Research partially supported by the Edmund Landau Center for Research in Mathematical Analysis and related areas, sponsored by Minerva Foundation (Germany).The space K[0, 1] of differences of convex functions on the closed interval [0, 1] is investigated as a dual Banach space. It is proved that a continuous function f on [0, 1] belongs to K[0, 1]
The space of entire functions of two variables as a metric space.