Related papers: Off-diagonal estimates for commutators of bi-param…

In this paper, the boundedness properties of commutators generated by $b$ and intrinsic square functions in the endpoint case are discussed, where $b\in BMO(\mathbb R^n)$. We first establish the weighted weak $L\log L$-type estimates for…

In this paper we study maximal directional singular integral operators in $ \mathbb{R}^n $ given by a H\"ormander--Mihlin multiplier on an $ (n-1)$-dimensional subspace and acting trivially in the perpendicular direction. The subspace is…

We present a unified method to obtain weighted estimates of linear and multilinear commutators with BMO functions, that is amenable to a plethora of operators and functional settings. Our approach elaborates on a commonly used Cauchy…

We obtain estimates of commutators of singular integral operators in Lipschitz spaces and apply the results to boundary regularity of elliptic equations in the plane. We obtain an explicit asymptotic formula for the Bergman projection.

We introduce an analogue of Calder\'on's first commutator along a parabola, and establish its $L^2$ boundedness under essentially sharp hypotheses.

In this paper we investigate the boundedness of sublinear operators generated by fractional integrals as well as sublinear operators generated by Calder\`on-Zygmund operators on generalized weighted Morrey spaces and generalized weighted…

In this note we study the $L^p-L^q$ boundedness of Fourier multipliers of anharmonic oscillators, and as a consequence also of spectral multipliers, for the range $1<p \leq 2 \leq q <\infty$. The underlying Fourier analysis is associated…

In the context of a finite measure metric space whose measure satisfies a growth condition, we prove "T1" type necessary and sufficient conditions for the boundedness of fractional integrals, singular integrals, and hypersingular integrals…

In this paper, we study the boundedness properties of the (dyadic) maximal bilinear operator associated with rough homogeneous kernels on $\mathbb{R}$. We establish sharp $L^{p_1}(\mathbb{R}) \times L^{p_2}(\mathbb{R}) \to…

Let $T_\Omega$ be the singular integral operator with variable kernel $\Omega(x,z)$. In this paper, by using the atomic decomposition theory of weighted weak Hardy spaces, we will obtain the boundedness properties of $T_\Omega$ on these…

In the paper, we study a kind of Oscillatory singular integral operator with Calder\'{o}n Type Commutators $T_{P,K,A} $ defined by \[T_{P,K,A} f(x)=\text { p.v.} \int_{\mathbb{R}^{n}} f(y) \frac{K(x-y)}{|x-y|}(A(x)-A(y)-\nabla A(y))(x-y)…

We obtain a necessary and sufficient condition on a polynomial $P(t_1,t_2)$ for the $\ell^{p}$ boundedness of the discrete double Hilbert transforms associated with $P(t)$ for $1 < p < \infty$. The proof is based on the multi-parameter…

Dyadic fractional integral operators are shown to be bounded on Morrey spaces and their preduals. It seems that the proof of the boundedness by means of dyadic fractional integral operators is effective particularly on the preduals. In the…

In this paper we establish some companions of perturbed Ostrowski type integral inequalities for functions whose second derivatives are bounded. Some applications to composite quadrature rules, and to probability density functions are also…

Multilinear $L^p$ extrapolation results are established in a limited-range, multilinear, and off-diagonal setting for mixed-norm Lebesgue spaces over $\sigma$-finite measure spaces. Integrability exponents are allowed in the full range…

In this paper, we establish the boundedness of the commutators of multilinear Hausdorff operators on the product of some weighted Morrey-Herz type spaces with variable exponent with their symbols belong to both Lipschitz space and central…

We describe the set of parameters $(p_1,p_2,q_1,q_2)$ such that the balls $B_{q_1,q_2}^{s,b}$ are rigid in $\ell_{q_1,q_2}^{s,b}$ metric i.e. they are poorly approximated by linear subspaces of dimension $\le (1-\varepsilon)sb$, for large…

In this paper we investigate boundedness, polar decomposition and spectral decomposition of weighted conditional expectation type operators on L^2(\Sigma).

We investigate the local boundedness of solutions $u:\Omega_T\to\mathbb{R}$ to parabolic equations of the form \begin{equation*} \partial_tu-\mathrm{div}\,\mathcal{A}(x,t,Du)=0 \qquad\mbox{in }\Omega_T=\Omega\times(0,T) \end{equation*} that…

We prove new results for multi-parameter singular integrals. For example, we prove that bi-parameter singular integrals in $\mathbb{R}^{n+m}$ satisfying natural $T1$ type conditions map $L^q(\mathbb{R}^n; L^p(\mathbb{R}^m;E))$ to…