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Weak and extra-weak type inequalities for the maximal operator and the Hilbert transform

Amiran Gogatishvili, Luboš Pick (1993)

Czechoslovak Mathematical Journal

Weak solution for fractional order integral equations in reflexive Banach spaces

Hussein A. H. Salem, Ahmed M. A. El-Sayed (2005)

Mathematica Slovaca

Weak solutions of differential equations in Banach spaces

Mieczysław Cichoń (1995)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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.

Stepanov, V.D., Ushakova, E.P. (2004)

Sibirskij Matematicheskij Zhurnal

Weighted estimates for the Riemann-Liouville operators with variable limits.

Prokhorov, D. V. (2003)

Sibirskij Matematicheskij Zhurnal

Weighted exponential inequalities.

Heinig, H.P., Kerman, R., Krbec, M. (2001)

Georgian Mathematical Journal

Weighted Friedrichs inequalities in amalgams

Hans P. Heinig, Alois Kufner (1993)

Czechoslovak Mathematical Journal

Weighted geometric mean inequalities over cones in $ℝ^{N}$ .

Gupta, Babita, Jain, Pankaj, Persson, Lars-Erik, Wedestig, Anna (2003)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Weighted inequalities for commutators of one-sided singular integrals

María Lorente, María Silvina Riveros (2002)

Commentationes Mathematicae Universitatis Carolinae

We prove weighted inequalities for commutators of one-sided singular integrals (given by a Calder’on-Zygmund kernel with support in $(- \infty, 0)$ ) 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.

Amiran Gogatishvili, Bohumir Opic, Lubos Pick (2006)

Collectanea Mathematica

Weighted integral inequalities with the geometric mean operator.

Persson, Lars-Erik, Stepanov, Vladimir D. (2002)

Journal of Inequalities and Applications [electronic only]

Weighted $L_{Φ}$ integral inequalities for operators of Hardy type

Steven Bloom, Ron Kerman (1994)

Studia Mathematica

Necessary and sufficient conditions are given on the weights t, u, v, and w, in order for $Φ_{2}^{- 1} (ʃ Φ_{2} (w (x) | T f (x) |) t (x) d x) \leq Φ_{1}^{- 1} (ʃ Φ_{1} (C u (x) | f (x) |) v (x) d x)$ to hold when $Φ_{1}$ and $Φ_{2}$ are N-functions with $Φ_{2} \circ Φ_{1}^{- 1}$ 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

Tatjana Ostrogorski (1998)

Colloquium Mathematicae

When is a Riesz distribution a complex measure?

Alan D. Sokal (2011)

Bulletin de la Société Mathématique de France

Let $ℛ_{α}$ be the Riesz distribution on a simple Euclidean Jordan algebra, parametrized by $α \in ℂ$ . I give an elementary proof of the necessary and sufficient condition for $ℛ_{α}$ to be a locally finite complex measure (= complex Radon measure).

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