On the existence and uniqueness of integrable solutions of functional equations in Banach space.
On the existence of a fundamental total and bounded biorthogonal sequence in every separable Banach space, and related constructions of uniformly bounded orthonormal systems in L²
On the existence of continuous modifications of vector-valued random fields.
On the existence of exactly one solution of integral equations in the space with a mixed norm
On the existence of Schauder bases in Sobolev spaces
On the Existence of Sub-Markovian Resolvents.
On the Existence of Uniformly Distributed Sequences in Compact Topological Spaces II.
On the expansion theorem described by spaces.
On the exponential Orlicz norms of stopped Brownian motion
Necessary and sufficient conditions are found for the exponential Orlicz norm (generated by with 0 < p ≤ 2) of or to be finite, where is a standard Brownian motion and τ is a stopping time for B. The conditions are in terms of the moments of the stopping time τ. For instance, we find that as soon as for some constant C > 0 as k → ∞ (or equivalently ). In particular, if τ ∼ Exp(λ) or then the last condition is satisfied, and we obtain with some universal constant K > 0....
On the extension of Lipschitz maps with values in a Fréchet space
On the extension of Lipschitz-Hölder maps on spaces
On the extension of Lipschitz-Hölder maps on Orlicz spaces
On the extrema of integrable functions.
On the extremal points of the closed unit balls in some abstract spaces
On the Extreme Points and Strongly Extreme Points in Köther-Bochner Spaces
On the Forelli-Rudin construction and weighted Bergman projections
On the generalized Hardy spaces.
On the generalized Hardy's inequality of McGhee, Pigno and Smith and the problem of interpolation between BMO and a Besov space.
On the generalized Morrey spaces.
On the Gram-Schmidt orthonormalizatons of subsystems of Schauder systems
In one of the earliest monographs that involve the notion of a Schauder basis, Franklin showed that the Gram-Schmidt orthonormalization of a certain Schauder basis for the Banach space of functions continuous on [0,1] is again a Schauder basis for that space. Subsequently, Ciesielski observed that the Gram-Schmidt orthonormalization of any Schauder system is a Schauder basis not only for C[0,1], but also for each of the spaces , 1 ≤ p < ∞. Although perhaps not probable, the latter result would...