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Generalized parabolic Marcinkiewicz integrals associated with polynomial compound curves with rough kernels

Ali Mohammed, Katatbeh Qutaibeh

Demonstratio Mathematica

2020

Vol. 53, nr 1

44--57

In this article, we study the generalized parabolic parametric Marcinkiewicz integral operators M(r)Ω,h,Φ,λ related to polynomial compound curves. Under some weak conditions on the kernels, we establish appropriate estimates of these operators. By the virtue of the obtained estimates along with an extrapolation argument, we give the boundedness of the aforementioned operators from Triebel-Lizorkin spaces to Lp spaces under weaker conditions on Ω and h. Our results represent significant improvements and natural extensions of what was known previously.

Remark on borderline traces of Besov and Triebel-Lizorkin spaces on noncompact hypersurfaces

Skrzypczak L., Tomasz B.

Commentationes Mathematicae

2013

Vol. 53, No. 2

193--209

We investigate borderline traces of Besov and Triebel-Lizorkin spaces. The function spaces are defined on noncompact Riemannian manifolds with bounded geometry. We described spaces of traces on noncompact submanifolds that are also of bounded geometry.