Nonlinear integration on Lp-spaces

Representation of nonlinear transformations and functionals on LP spaces

Totally probabilistic Lp spaces

In this paper, we introduce the notion of probabilistic valued measures as a generalization of non-negative measures and construct the corresponding Lp spaces, for distributions p > "0. It is alsoshown that if the distribution p satises p "1 then, as in the classical case, these spaces are completeprobabilistic normed spaces.

On convex risk measures on Lp-spaces

Much of the recent literature on risk measures is concerned with essentially bounded risks in L∞. In this paper we investigate in detail continuity and representation properties of convex risk measures on L spaces. This frame for risks is natural from the point of view of applications since risks are typically modelled by unbounded random variables. The various continuity properties of risk mea...

Norms of Positive Operators on LP-Spaces

Let 0 < T: LP(Y, v) -+ Lq(X, ) be a positive linear operator and let HITIP ,q denote its operator norm. In this paper a method is given to compute 1Tllp, q exactly or to bound 11Tllp q from above. As an application the exact norm 11VIlp,q of the Volterra operator Vf(x) = fo f(t)dt is computed.

MULTIRESOLUTION OF Lp SPACES

Multiresolution analysis plays a major role in wavelet theory. In this paper, multiresolution of Lp spaces is studied. Let S be a shift-invariant subspace of Lp(IR) (1 ≤ p ≤ ∞) generated by a finite number of functions with compact support, and let Sk be the 2-dilate of S for each integer k ∈ ZZ. It is shown that the intersection of Sk (k ∈ ZZ) is always trivial. It is more difficult to deal wi...