Related papers: A weak type estimate for regular fractional sparse…

For a class of sparse operators including majorants of singular integral, square function, and fractional integral operators in a uniform manner, we prove off-diagonal two-weight estimates of mixed type in the two-weight and…

In this paper, we state with a variational method a general theorem providing the existence of a weak solution $u$ for fractional Euler-Lagrange equations of the type: $$ \dfrac{\partial L}{\partial x} (u,D^\alpha_- u,t) + D^\alpha_+…

Let $L f(x):=-\frac{d^2}{dx^2}f(x)-\frac{ r}{x}\frac{d}{dx}f(x),\quad x>0, r>0$ be the Bessel operator on $((0,\infty), |\cdot|, x^rdx)$. In this paper, we prove the sharp weak type $(1,1)$ estimate for the imaginary power $L^{i\alpha},…

The numerical approximation of the solution to a stochastic partial differential equation with additive spatial white noise on a bounded domain is considered. The differential operator is assumed to be a fractional power of an integer order…

Instrumental variables estimation has gained considerable traction in recent decades as a tool for causal inference, particularly amongst empirical researchers. This paper makes three contributions. First, we provide a detailed theoretical…

In this paper, we study the weighted inequality for multilinear fractional maximal operators and fractional integrals. We give sharp weighted estimates for both operators.

We investigate inexact proximity operators for weakly convex functions. To this aim, we derive sum rules for proximal {\epsilon}-subdifferentials, by incorporating the moduli of weak convexity of the functions into the respective formulas.…

We study the fundamental problem of the calculus of variations with variable order fractional operators. Fractional integrals are considered in the sense of Riemann-Liouville while derivatives are of Caputo type.

In this paper, we estimate the high dimensional precision matrix under the weak sparsity condition where many entries are nearly zero. We revisit the sparse column-wise inverse operator (SCIO) estimator \cite{liu2015fast} and derive its…

We will give some regularity results about fractional diffusion-wave equations.

We investigate algebraic properties of weakly commutative triples, appearing in the theory of integrable nonlinear partial differential equations. Algebraic technique of skew fields of formal pseudodifferential operators as well as skew Ore…

We study the boundedness of certain fractional integral operators from Hp(.) into Lq(.). We also obtain the Hp(.)- Hq(.) boundedness of the Riesz potential.

This paper gives the pointwise sparse dominations for variation operators of singular integrals and commutators with kernels satisfying the $L^r$-H\"{o}rmander conditions. As applications, we obtain the strong type quantitative weighted…

We introduce a new class of fractional backward orthogonal functions designed for the spectral approximation of weakly singular adjoint Volterra integral equations. These basis functions generate an approximation space that naturally…

We present a new numerical tool to solve partial differential equations involving Caputo derivatives of fractional variable order. Three Caputo-type fractional operators are considered, and for each one of them an approximation formula is…

We give an exact formula for the Bellman function of the weak type of martingale transform. We also give the extremal functions (actually extremal sequences of functions). We find them using the precise form of the Bellman function. The…

We obtain $H^{p}_{w} - L^{q}_{w^{q/p}}$ estimates for certain fractional operators.

Although the study of functional calculus has already established necessary and sufficient conditions for operators to be fractionalized, this paper aims to use our well-conceived notion of integer powers of operators to construct…

In this paper we study some properties of the Prabhakar integrals and derivatives and of some of their extensions such as the regularized Prabhakar derivative or the Hilfer--Prabhakar derivative. Some Opial- and Hardy-type inequalities are…

Let $L$ be a closed, densely defined operator on $L^2(\mathbb{R}^n)$ satisfying suitable $L^p-L^q$ off-diagonal estimates of order $\kappa > 0$. This paper aims to investigate the two-weight estimate and the Bloom weighted estimate for the…