Asymptotic properties of solutions of the differential equation $\lbrace A^{-1}_{n-1}(t)\dots [A^{-1}_1(t)y^{\prime }]^{\prime }\dots \rbrace ^{\prime }=A_n(t)y+F(t)$

Ivo Res

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We consider operators of the form $(Ω f) (y) = ʃ_{- \infty}^{\infty} Ω (y, u) f (u) d u$ with Ω(y,u) = K(y,u)h(y-u), where K is a Calderón-Zygmund kernel and $h \in L^{\infty}$ (see (0.1) and (0.2)). We give necessary and sufficient conditions for such operators to map the Besov space $Ḃ_{1}^{0, 1}$ (= B) into itself. In particular, all operators with $h (y) = e^{{i | y |}^{a}}$ , a > 0, a ≠ 1, map B into itself.

Displaying similar documents to “Asymptotic properties of solutions of the differential equation { A n - 1 - 1 ( t ) ⋯ [ A 1 - 1 ( t ) y ' ] ' ⋯ } ' = A n ( t ) y + F ( t ) ”

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Nonconvolution transforms with oscillating kernels that map Ḃ 1 0 , 1 into itself

Displaying similar documents to “Asymptotic properties of solutions of the differential equation ${A_{n - 1}^{- 1} (t) \dots {[A_{1}^{- 1} (t) y^{'}]}^{'} \dots}^{'} = A_{n} (t) y + F (t)$ ”

Asymptotic formulas for solutions of the equation ${[p (t) y^{'}]}^{'} = q (t) y + r (t)$

Nonconvolution transforms with oscillating kernels that map $Ḃ_{1}^{0, 1}$ into itself