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In this paper, we are interested in the following bilinear fractional integral operator $Bmathcal{I}_alpha$ defined by [ Bmathcal{I}_{alpha}({f,g})(x)=int_{% %TCIMACRO{U{211d} }% %BeginExpansion mathbb{R} %EndExpansion ^{n}}frac{f(x-y)g(x+y)}{|y|^{n-alpha}}dy, ] with $0< alpha<n$. We prove the weighted boundedness of $Bmathcal{I}_alpha$ on the Morrey type spaces. Moreover, an Olsen type inequality for $Bmathcal{I}_alpha$ is also given.
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}_{+
We consider singular integral operators and maximal singular integral operators with rough kernels on homogeneous groups. We prove certain estimates for the operators that imply $L^p$ boundedness of them by an extrapolation argument under a sharp con
We find a minimal notion of non-degeneracy for bilinear singular integral operators $T$ and identify testing conditions on the multiplying function $b$ that characterize the $L^ptimes L^qto L^r,$ $1<p,q<infty$ and $r>frac{1}{2},$ boundedness of the b
We prove the endpoint weak type estimate for square functions of Marcinkiewicz type with fractional integrals associated with non-isotropic dilations. This generalizes a result of C. Fefferman on functions of Marcinkiewicz type by considering fractio
We study the bilinear Hilbert transform and bilinear maximal functions associated to polynomial curves and obtain uniform $L^r$ estimates for $r>frac{d-1}{d}$ and this index is sharp up to the end point.