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Translation-invariant operators on Lorentz spaces L(1,q) with 0 < q < 1

Leonardo Colzani, Peter Sjögren (1999)

Studia Mathematica

We study convolution operators bounded on the non-normable Lorentz spaces L 1 , q of the real line and the torus. Here 0 < q < 1. On the real line, such an operator is given by convolution with a discrete measure, but on the torus a convolutor can also be an integrable function. We then give some necessary and some sufficient conditions for a measure or a function to be a convolutor on L 1 , q . In particular, when the positions of the atoms of a discrete measure are linearly independent over the rationals,...

Triangular Models and Asymptotics of Continuous Curves with Bounded and Unbounded Semigroup Generators

Kirchev, Kiril, Borisova, Galina (2005)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary 47A48, Secondary 60G12.In this paper classes of K^r -operators are considered – the classes of bounded and unbounded operators A with equal domains of A and A*, finite dimensional imaginary parts and presented as a coupling of a dissipative operator and an antidissipative one with real absolutely continuous spectra and the class of unbounded dissipative K^r -operators A with different domains of A and A* and with real absolutely continuous spectra....

Trichotomy and bounded solutions of nonlinear differential equations

Mieczysław Cichoń (1994)

Mathematica Bohemica

The existence of bounded solutions for equations x ' = A ( t ) x + f ( t , x ) in Banach spaces is proved. We assume that the linear part is trichotomic and the perturbation f satisfies some conditions expressed in terms of measures of noncompactness.

Triebel-Lizorkin spaces with non-doubling measures

Yongsheng Han, Dachun Yang (2004)

Studia Mathematica

Suppose that μ is a Radon measure on d , which may be non-doubling. The only condition assumed on μ is a growth condition, namely, there is a constant C₀ > 0 such that for all x ∈ supp(μ) and r > 0, μ(B(x,r)) ≤ C₀rⁿ, where 0 < n ≤ d. The authors provide a theory of Triebel-Lizorkin spaces p q s ( μ ) for 1 < p < ∞, 1 ≤ q ≤ ∞ and |s| < θ, where θ > 0 is a real number which depends on the non-doubling measure μ, C₀, n and d. The method does not use the vector-valued maximal function inequality...

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