Wyniki wyszukiwania

1

Compactness of Hardy-type integral operators in weighted Banach function spaces

100%

E. Edmunds D., Gurka P., Pick L.

Studia Mathematica

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1994

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tom 109

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nr 1

73-90

EN

We consider a generalized Hardy operator $Tf(x) = ϕ(x) ʃ_{0}^{x} ψfv$. For T to be bounded from a weighted Banach function space (X,v) into another, (Y,w), it is always necessary that the Muckenhoupt-type condition $ℬ = sup_{R>0} ∥ϕχ_{(R,∞)}∥_{Y}∥ψχ_{(0,R)}∥_{X'} < ∞$ be satisfied. We say that (X,Y) belongs to the category M(T) if this Muckenhoupt condition is also sufficient. We prove a general criterion for compactness of T from X to Y when (X,Y) ∈ M(T) and give an estimate for the distance of T from the finite rank operators. We apply the results to Lorentz spaces and characterize pairs of Lorentz spaces which fall into M (T).

2

Periodic solutions for quasilinear vector differential equations with maximal monotone terms

63%

Kourogenis N., Papageorgiou N.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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1997

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tom 17

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nr 1-2

67-81

EN

We consider a quasilinear vector differential equation with maximal monotone term and periodic boundary conditions. Approximating the maximal monotone operator with its Yosida approximation, we introduce an auxiliary problem which we solve using techniques from the theory of nonlinear monotone operators and the Leray-Schauder principle. To obtain a solution of the original problem we pass to the limit as the parameter λ > 0 of the Yosida approximation tends to zero.

3

The geometry of Kato Grassmannians

63%

Bojarski B., Khimshiashvili G.

Open Mathematics

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2005

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tom 3

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nr 4

705-717

EN

We discuss Fredholm pairs of subspaces and associated Grassmannians in a Hilbert space. Relations between several existing definitions of Fredholm pairs are established as well as some basic geometric properties of the Kato Grassmannian. It is also shown that the so-called restricted Grassmannian can be endowed with a natural Fredholm structure making it into a Fredholm Hilbert manifold.

Ograniczanie wyników

1 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Open Mathematics

1 Studia Mathematica

1 Bojarski B.

1 E. Edmunds D.

1 Gurka P.

1 Khimshiashvili G.

1 Kourogenis N.

1 Papageorgiou N.

1 Pick L.

1 2005

1 1997

1 1994

Compactness of Hardy-type integral operators in weighted Banach function spaces

Periodic solutions for quasilinear vector differential equations with maximal monotone terms

The geometry of Kato Grassmannians