Lech Maligranda

Generalized duality of some Banach function spaces

Abstract The set of multipliers from one vector space to another vector space may be seen as a generalized dual space in the sense of Kothe. We give some properties of this kind of duality and prove precise estimates concerning generalized duality of X P -spaces, Lebesgue, Lorentz, Marcinkiewicz and Orlicz spaces. We complement and unify several previous results of this kind.

On Some Properties of Functions of Generalized Variation

We show that the spaceVφ* generated by a φ-variation (or φ-variation of Riesz, or λ-variation of Waterman) forms a commutative Banach algebra with respect to the pointwise multiplication under the appropriate choice of norms.

On an elementary approach to the fractional Hardy inequality

Let be the usual Hardy operator, i.e., . We prove that the operator is bounded and has a bounded inverse on the weighted spaces for -1

Multiplicative inequalities of Carlson type and interpolation

type=#_x005F_x0000_t75>and . Moreover, by using these ineq ...

Interpolation between sum and intersection of Banach spaces

Carlsons Inequalities Some Extensions and Complements to Carlsons Inequalities The Continuous Case Levins Theorem Some Multi-Dimensional Generalizations and Variations Some Carlson Type Inequalities for Weighted Lebesgue Spaces with General Measures Carlson Type Inequalities and Real Interpolation Theory Further Connection to Interpolation Theory, the Peetre Method Related Results and Applications Appendices: A Historical Note on Fritz David Carlson (1888-1952) A Translation of the Original Article by Carlson from French to English.

A submultiplicative function

Abstract We study intermediate Banach spaces A which are or are not interpolation spaces between A 0 + A 1 and A 0 ∩ A 1 .

Landau type theorem for Orlicz spaces

Let a≥1 and fa (x)=ln(x+a). It is shown that the function fa is submultiplicative on [0,∞) if and only if a ≥ e. 2. Moreover, the function fa is submultiplicative on [1,∞) if and only if a ≥ ao = 1.7550696584…The techniques the authors describe can also be used for other functions f different from fa.

Weakly Compact Operators and Interpolation

In this paper the authors discuss Landaus theorem presenting an inverse of the classical Holder-type inequality for sequence and function spaces.The results given are for Orlicz spaces and their g ...

The E-Functional for Some Pairs of Groups

The class of weakly compact operators is, as well as the class of compact operators, a fundamental operator ideal. They were investigated strongly in the last twenty years. In this survey, we have collected and ordered some of this (partly very new) knowledge. We have also included some comments, remarks and examples.

Notes on non-interpolation spaces

We describe a new algorithm to compute the eigenvalues of singular Sturm-Liouville problems with separated self-adjoint boundary conditions for both the limit-circle nonoscillatory and oscillatory cases. Also described is a numerical code implementing this algorithm and how it compares with SLEIGN. The latter is the only effective general purpose software available for the computation of the eigenvalues of singular Sturm-Liouville problems.