Weak and extra-weak type inequalities for the maximal operator and the Hilbert transform
Weak solution for fractional order integral equations in reflexive Banach spaces
Weak solutions of differential equations in Banach spaces
In this paper we prove a theorem for the existence of pseudo-solutions to the Cauchy problem, x' = f(t,x), x(0) = x₀ in Banach spaces. The function f will be assumed Pettis-integrable, but this assumption is not sufficient for the existence of solutions. We impose a weak compactness type condition expressed in terms of measures of weak noncompactness. We show that under some additionally assumptions our solutions are, in fact, weak solutions or even strong solutions. Thus, our theorem is an essential...
Weighted estimates for the integral operators with monotone kernel on a half-axis.
Weighted estimates for the Riemann-Liouville operators with variable limits.
Weighted exponential inequalities.
Weighted Friedrichs inequalities in amalgams
Weighted geometric mean inequalities over cones in .
Weighted inequalities for commutators of one-sided singular integrals
We prove weighted inequalities for commutators of one-sided singular integrals (given by a Calder’on-Zygmund kernel with support in ) with BMO functions. We give the one-sided version of the results in C. Pérez, Sharp estimates for commutators of singular integrals via iterations of the Hardy-Littlewood maximal function, J. Fourier Anal. Appl., vol. 3 (6), 1997, pages 743–756 and C. Pérez, Endpoint estimates for commutators of singular integral operators, J. Funct. Anal., vol 128 (1), 1995, pages...
Weighted inequalities for Hardy-type operators involving suprema.
Weighted integral inequalities with the geometric mean operator.
Weighted integral inequalities for operators of Hardy type
Necessary and sufficient conditions are given on the weights t, u, v, and w, in order for to hold when and are N-functions with convex, and T is the Hardy operator or a generalized Hardy operator. Weak-type characterizations are given for monotone operators and the connection between weak-type and strong-type inequalities is explored.
Weighted norm inequalities and homogeneous cones
When is a Riesz distribution a complex measure?
Let be the Riesz distribution on a simple Euclidean Jordan algebra, parametrized by . I give an elementary proof of the necessary and sufficient condition for to be a locally finite complex measure (= complex Radon measure).