# Eigenvalue problems with weights in Lorentz spaces

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We show that the inverse of a planar homeomorphism of bounded variation is also of bounded variation. In higher dimensions we show that f -1 is of bounded variation provided that f ? W 1,1(O; R n ) is a homeomorphism with | Df| in the Lorentz space L n-1,1(O).

- The Fourier-Walsh series of the functions absolutely continuous in the generalized restricted sense. Lukomskii, S. F. // Siberian Mathematical Journal;Mar2007, Vol. 48 Issue 2, p273
We consider the questions of convergence in Lorentz spaces for the Fourier-Walsh series of the functions with Denjoy integrable derivative. We prove that a condition on a function f sufficient for its Fourier-Walsh series to converge in the Lorentz spaces ï¿½nearï¿½ L 8 cannot be expressed...

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We consider the questions of convergence of Fourier-Walsh series in Lorentz spaces. Some condition is given on a function Æ’ sufficient for its Fourier-Walsh series to converge in the Lorentz spaces â€œnearâ€ L âˆž. We show that this result is sharp.

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A procedure is given to reduce the interpolation spaces on an ordered pair generated by the function parameter $t^{\theta}(1+|\hspace{-2pt}\log t|)^{-b}$ to the classical real interpolation spaces. Applications are given for LorentzÂ–Zygmund function spaces, Besov spaces of generalized...

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Let Î© âŠ‚ Rn be a domain. The result of J. Kauhanen, P. Koskela and J. MalÃ½ [4] states that a function Æ’ : Î© â†’ R with a derivative in the Lorentz space Ln,Â¹ (Î©, Rn) is n-absolntely continuous in the sense of [5]. We give an example of an absolutely continuous...

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The Lorentz lemma is generalized to the case of the media with arbitrary form of the spatial dispersion. Correctness of the obtained relation is confirmed by calculation of the radiation fields of a point source in a moving strongly magnetized plasma.

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We give a complete classification of surfaces with parallel second fundamental form in Lorentzian real space forms of dimension three and four.

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This paper discusses the positivity preserving interpolation for positive surfaces data by extending the C1 rational cubic spline interpolant of Karim and Kong to the bivariate cases. The partially blended rational bicubic spline has 12 parameters in the descriptions where 8 of them are free...

- Two-Weight Extrapolation on Lorentz Spaces. Li, Wenming; Zhang, Tingting; Xue, Limei // Journal of Function Spaces;1/1/2015, Vol. 2015, p1
We give several two-weight extrapolation theorems on Lorentz spaces which extend the results of Cruz-Uribe and PÃ©rez (2000) and some applications for the singular integral operators, the potential type operators, and commutators.