A priori inequalities in $L ^\infty (\Omega )$ for solutions of elliptic equations in unbounded domains

Maurizio Chicco; Marina Venturino

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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.

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Displaying similar documents to “A priori inequalities in L ∞ ( Ω ) for solutions of elliptic equations in unbounded domains”

Displaying similar documents to “A priori inequalities in $L^{\infty} (Ω)$ for solutions of elliptic equations in unbounded domains”