Analysis Mathematica最新文献

In this paper, we provide sufficient conditions for the functions ( psi ) and ( phi ) to be the approximate duals in the Hardy space (H^p(mathbb{R})) for all ( 0<ple 1 ).Based on these conditions, we obtain the wavelet series expansion in the Hardyspace (H^p(mathbb{R})) with the approximate duals. The important properties of our approachinclude the following: (i) our results work for any ( 0<p leq 1 ); (ii) we do notassume that the functions ( psi ) and ( phi ) are exact duals; (iii) we provide a tractablebound for the operator norm of the associated wavelet frame operator so that itis possible to check the suitability of the functions ( psi ) and ( phi ).

We study composition operators between variable exponentLebesgue spaces and characterize boundedness and compactness of the composition operators on a variable exponent Lebesgue space. We also derive a sufficient condition for composition operator to have a closed range and explain someproperties which these operators share with the case of Lebesgue spaces.

The core of a compact set in a general complex manifold has beendefined by Shcherbina very recently to study the existence of strictly plurisubharmonic functions on compact sets. In this paper, using m-subharmonic functionson compact subsets of a non-compact Kähler manifold, we define the set m-coreof a compact set and investigate the structure of it.

We will have the decomposition of the m-minimal kernel of a weaklym-complete manifold and show that it can be fully decomposed into compactm-pseudoconcave subsets via certain results obtained in the author’s very recentpapers to have the disintegration of the set m-core of the entire Kähler manifold(or of a domain in the manifold) and to study the characterization of so-calledm-Stein manifolds.

Let (b) be a locally integrable function and (mathfrak{M}) be the bilinear maximal function

In this paper, characterization of the BMO function in terms of commutator (mathfrak{M}^{(1)}_{b}) is established. Also, we obtain the necessary and sufficient conditions for the boundedness of the commutator ([b, mathfrak{M}]_{1}). Moreover, some new characterizations of Lipschitz and non-negative Lipschitz functions are obtained.

We prove that a uniformly convergent trigonometric series may not satisfy the permutation sign convergence condition, hence it may not satisfy the Rademacher condition as well.

Suppose X and Y are Banach spaces, K is a compact Hausdorff space, (Sigma) is the (sigma)-algebra of Borel subsets of K, (C(K,X)) is the Banach space of all continuous X-valued functions (with the supremum norm), and (T colon C(K,X)to Y) is a strongly bounded operator with representing measure (m colon Sigma to L(X,Y)). We show that if (hat{T} colon B(K, X) to Y) is its extension, then T is weak Dunford--Pettis (resp.weak^* Dunford--Pettis, weak p-convergent, weak^* p-convergent) if and only if (hat{T}) has the same property.

We prove that if (T colon C(K,X)to Y) is strongly bounded limited completely continuous (resp. limited p-convergent), then (m(A) colon Xto Y) is limited completely continuous (resp. limited p-convergent) for each (Ain Sigma). We also prove that the above implications become equivalences when K is a dispersed compact Hausdorff space.

An interesting result due to Dilworth et al. was that if we enlargegreedy sums by a constant factor (lambda > 1) in the condition defining the greedyproperty, then we obtain an equivalence of the almost greedy property, a strictlyweaker property. Previously, the author showed that enlarging greedy sums by (lambda)in the condition defining the partially greedy (PG) property also strictly weakensthe property. However, enlarging greedy sums in the definition of reverse partiallygreedy (RPG) bases by Dilworth and Khurana again gives RPG bases. The companionof PG and RPG bases suggests the existence of a characterization of RPGbases which, when greedy sums are enlarged, gives an analog of a result that holdsfor partially greedy bases. In this paper, we show that such a characterizationindeed exists, answering positively a question previously posed by the author.

The sun dual space corresponding to a strongly continuous semigroup is a known concept when dealing with dual semigroups, which are in general only weak (^*)-continuous. In this paper we develop a corresponding theory for bi-continuous semigroups under mild assumptions on the involved locally convex topologies. We also discuss sun reflexivity and Favard spaces in this context, extending classical results by van Neerven.

Let (f) be an integrable function which has integral (0) on (mathbb{R}^n ).What is the largest condition on (|f|) that guarantees that (f) is in the Hardy space(mathcal{H}^1(mathbb{R}^n))? When (f) is compactly supported, it is well-known that the largest conditionon (|f|) is the fact that (|f|in L log L(mathbb{R}^n) ). We consider the same kind ofproblem here, but without any condition on the support. We do so for (mathcal{H}^1(mathbb{R}^n)),as well as for the Hardy space (mathcal{H}_{log}(mathbb{R}^n)) which appears in the study of pointwiseproducts of functions in (mathcal{H}^1(mathbb{R}^n)) and in its dual BMO.

This paper is devoted to study the interrelations between inessential, improjective, strictly singular and strictly cosingular linear relations. First, we show that the classes of strictly singular and strictly cosingular linear relations with finite dimensional multivalued part are contained in the class of inessential linear relations and that for many Banach spaces these inclusions are equalities. Moreover, we prove that the class of improjective linear relations contains the class of inessential linear relations and we also see that for the most classical Banach spaces the improjective linear relations with finite dimensional multivalued part coincide with the inessential linear relations with finite dimensional multivalued part. Finally, to give value to our results we construct an example of a closed everywhere defined linear relation with finite dimensional multivalued part of each of the following types: inessential not strictly singular. inessential not strictly cosingular. improjective not inessential.