Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSome estimates for the bilinear fractional integrals on the Morrey space
106
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
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.
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 condition for the kernels. Also, we prove some weighted $L^p$ inequalities for the operators.
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 bilinear commutator $[b,T]_1(f,g) = bT(f,g) - T(bf,g).$ Our arguments cover almost all arrangements of the integrability exponents $p,q,r,$ with a single open problem presented in the end. Additionally, the arguments extend to the multilinear setting.
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 fractional integrals of mixed homogeneity in place of the Riesz potentials of Euclidean structure.
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.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
