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تسجيل مستخدم جديدWeighted Weak (1,1) estimates for one-sided oscillatory singular integrals
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We consider one-sided weight classes of Muckenhoupt type and study the weighted weak type (1,1) norm inequalities of a class of one-sided oscillatory singular integrals with smooth kernel.
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The purpose of this paper is to establish some one-sided estimates for oscillatory singular integrals. The boundedness of certain oscillatory singular integral on weighted Hardy spaces $H^{1}_{+}(w)$ is proved. It is here also show that the $H^{1}_{+
}(w)$ theory of oscillatory singular integrals above cannot be extended to the case of $H^{q}_{+}(w)$ when $0<q<1$ and $win A_{p}^{+}$, a wider weight class than the classical Muckenhoupt class. Furthermore, a criterion on the weighted $L^{p}$-boundednesss of the oscillatory singular integral is given.
Let $ Tf =sum_{ I} varepsilon_I langle f,h_{I^+}rangle h_{I^-}$. Here, $ lvert varepsilon _Irvert=1 $, and $ h_J$ is the Haar function defined on dyadic interval $ J$. We show that, for instance, begin{equation*} lVert T rVert _{L ^{2} (w) to L ^{2}
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