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On very weak solutions of a class of nonlinear elliptic systems

Menita Carozza, Antonia Passarelli di Napoli (2000)

Commentationes Mathematicae Universitatis Carolinae

In this paper we prove a regularity result for very weak solutions of equations of the type - div A ( x , u , D u ) = B ( x , u , D u ) , where A , B grow in the gradient like t p - 1 and B ( x , u , D u ) is not in divergence form. Namely we prove that a very weak solution u W 1 , r of our equation belongs to W 1 , p . We also prove global higher integrability for a very weak solution for the Dirichlet problem - div A ( x , u , D u ) = B ( x , u , D u ) in Ω , u - u o W 1 , r ( Ω , m ) .

On weak topology of Orlicz spaces.

Shutao Chen, Huiying Sun (1993)

Collectanea Mathematica

This paper presents some properties of singular functionals on Orlicz spaces, from which criteria for weak convergence and weak compactness in such spaces are obtained.

On ω-convex functions

Tomasz Szostok (2011)

Banach Center Publications

In Orlicz spaces theory some strengthened version of the Jensen inequality is often used to obtain nice geometrical properties of the Orlicz space generated by the Orlicz function satisfying this inequality. Continuous functions satisfying the classical Jensen inequality are just convex which means that such functions may be described geometrically in the following way: a segment joining every pair of points of the graph lies above the graph of such a function. In the current paper we try to obtain...

One-weight weak type estimates for fractional and singular integrals in grand Lebesgue spaces

Vakhtang Kokilashvili, Alexander Meskhi (2014)

Banach Center Publications

We investigate weak type estimates for maximal functions, fractional and singular integrals in grand Lebesgue spaces. In particular, we show that for the one-weight weak type inequality it is necessary and sufficient that a weight function belongs to the appropriate Muckenhoupt class. The same problem is discussed for strong maximal functions, potentials and singular integrals with product kernels.

Operators on Lorentz sequence spaces

Subhash Chander Arora, Gopal Datt, Satish Verma (2009)

Mathematica Bohemica

Description of multiplication operators generated by a sequence and composition operators induced by a partition on Lorentz sequence spaces l ( p , q ) , 1 < p , 1 q is presented.

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