Abstract. In this paper, we provide a version of the Mihlin-Hörmander multiplier theorem for multilinear operators in the case where the target space is L p for p ≤ 1. This extends a recent result of Tomita [15] who proved an analogous result for p > 1.
We establish the Triebel-Lizorkin boundedness for a class of singular integral operators associated to surfaces of revolution, {( , ( )) : ∈ ℝ }, with rough kernels Ω, provided that the corresponding maximal function along the plane curve {( , ( )) : ∈ ℝ} is bounded on (ℝ 2 ). We treat kernel functions belonging to a generalized function space relating to Grafakos and Stefanov's F ( −1 ) spaces.
LetLbe the infinitesimal generator of an analytic semigroup onL2(Rn)with Gaussian kernel bounds, and letL-α/2be the fractional integrals ofLfor0<α<n. For any locally integrable functionb, the commutators associated withL-α/2are defined by[b,L-α/2](f)(x)=b(x)L-α/2(f)(x)-L-α/2(bf)(x). Whenb∈BMO(ω)(weightedBMOspace) orb∈BMO, the authors obtain the necessary and sufficient conditions for the boundedness of[b,L-α/2]on weighted Morrey spaces, respectively.
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