A weight space invariant with respect to a singular linear operator |
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Authors: | A Ya Yakubov |
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Institution: | 1. Dagestan Polytechnic Institute, USSR
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Abstract: | For the singular operator $$Su = \int_a^b {\frac{{K(x, s) u (s)}}{{s - x}}} ds$$ invariant weight spacesλ α β , p (u(x)∈λ α β , p if 10,u (x) ρ (x)∈ H β 0 , 20.‖u‖L p(ρ0)<∞, ρ (x) = (x?a) (b ?x)1+β, ρ0(x)=(b?x)α(p?1), 0<α, β<1,p>1H 0 β is a Hölder space. Multiplicative inequalities of the type of Kh. Sh. Mukhtarov are also obtained. |
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