Commutators of the Fractional Hardy Operator on Weighted Variable Herz-Morrey Spaces

In the present paper, our aim is to establish the boundedness of commutators of the fractional Hardy operator and its adjoint operator on weighted Herz-Morrey spaces with variable exponents M K ̇ p , q ⋅ α ⋅ , λ w .

Boundedness for Commutators of Rough p -Adic Hardy Operator on p -Adic Central Morrey Spaces

In the present article we obtain the boundedness for commutators of rough p -adic Hardy operator on p -adic central Morrey spaces. Furthermore, we also acquire the boundedness of rough p -adic Hardy operator on Lebesgue spaces.

Weighted Central BMO Spaces and Their Applications

In this paper, the central BMO spaces with Muckenhoupt A p weight is introduced. As an application, we characterize these spaces by the boundedness of commutators of Hardy operator and its dual operator on weighted Lebesgue spaces. The boundedness of vector-valued commutators on weighted Herz spaces is also considered.

The estimates of the approximation numbers of the Hardy operator acting in the Lorenz spaces in the case ${\it {\bf \max}(r,s)\leq q}$

In the paper conditions are found under which the compact operator $Tf(x)=\varphi(x)\int_0^ xf(\tau)v(\tau)\,d\tau,$ $x>0,$ acting in weighted Lorentz spaces $T:L^{r,s}_{v} (\mathbb{R^+})\to L^{p,q}_{\omega}(\mathbb{R^+})$ in the domain $1<\max (r,s)\le \min(p,q)<\infty,$ belongs to operator ideals $\mathfrak{S}^{(a)}_\alpha$ and $\mathfrak{E}_\alpha$, $0<\alpha<\infty$. And estimates are also obtained for the quasinorms of operator ideals in terms of integral expressions which depend on operator weight functions.

Weighted Estimates for Commutator of Rough p -Adic Fractional Hardy Operator on Weighted p -Adic Herz–Morrey Spaces

The current article investigates the boundedness criteria for the commutator of rough p -adic fractional Hardy operator on weighted p -adic Lebesgue and Herz-type spaces with the symbol function from weighted p -adic bounded mean oscillations and weighted p -adic Lipschitz spaces.

New characterizations of weights on dynamic inequalities involving a Hardy operator

In this paper, we establish some new characterizations of weighted functions of dynamic inequalities containing a Hardy operator on time scales. These inequalities contain the characterization of Ariňo and Muckenhoupt when $\mathbb{T}=\mathbb{R}$ T = R , whereas they contain the characterizations of Bennett–Erdmann and Gao when $\mathbb{T}=\mathbb{N}$ T = N .

Estimates for Commutators of Bilinear Fractional p -Adic Hardy Operator on Herz-Type Spaces

In the current article, we investigate the boundedness of commutators of the bilinear fractional p -adic Hardy operator on p -adic Herz spaces and p -adic Morrey-Herz spaces by considering the symbol function from central bounded mean oscillations and Lipschitz spaces.