This paper aims to show that the fractional Hardy operator and its adjoint are bounded on central Morrey space with variable exponent. Similar results for their commutators obtained when symbol functions belong λ -central mean oscillation ( id="M3"> BMO)

For {φ_n(x)}, x ε [0,1] an orthonormalsystem of uniformly bounded functions, ||φ_n||_{∞}≤ M

We obtain the characterizations of commutators several versions maximal functions on spaces homogeneous type. In addition, with aid interpolation theory, we provide weighted version commutator theorems by establishing new BMO space. Finally, a concrete example shows that local also has an independent interest.

Let (X, d, μ) be a metric measure space satisfying Q-doubling condition (Q > 1) and an L2-Poincaré inequality. $${\cal L} = {\cal + V$$ Schrödinger operator on X, where L}$$ is non-negative generalized by Dirichlet form, V Muckenhoupt weight that satisfies reverse Hölder RHq for some q ⩾ 1)/2. We show solution to $$({\cal - \partial _t^2)u 0$$ X × ℝ+ the Carleson $$\mathop {{\rm{sub}}}\limits_{...

Weighted L for p ∈ 1,∞ and weak-type endpoint estimates with general weights are established for commutators of the Hardy-Littlewood maximal operator with BMO symbols on spaces of homogeneous type. As an application, a weighted weak-type endpoint estimate is proved for maximal operators associated with commutators of singular integral operators with BMO symbols on spaces of homogeneous type. Al...

We establish a connection between the absolute continuity of elliptic measure associated to a second order divergence form operator with bounded measurable coefficients with the solvability of an endpoint BMO Dirichlet problem. We show that these two notions are equivalent. As a consequence we obtain an end-point perturbation result, i.e., the solvability of the BMO Dirichlet problem implies Lp...

The natural BMO (bounded mean oscillation) conditions suggested by scalar-valued results are known to be insufficient for the boundedness of operator-valued paraproducts. Accordingly, singular integrals has only been available under versions classical “T(1)?BMO” assumptions that not easily checkable. Recently, Hong, Liu and Mei (J. Funct. Anal. 2020) observed situation improves remarkably with ...

PURPOSE To observe the relationship between topographic hemoglobin levels in the optic nerve head (ONH), the rim thickness (BMO-MRW), and retinal nerve fiber layer (RNFL) thickness. METHODS 96 normal eyes and 82 glaucomas were examined using TOP strategy (Octopus 300 perimeter), SPECTRALIS OCT, and Laguna ONhE program which estimates hemoglobin from conventional color photographs (Horus Scope...

Let T be the Calderón-Zygmund operator, Coifman, Rochberg and Weiss (see [4]) proves that the commutator [b, T ](f) = bT (f) − T (bf)(where b ∈ BMO(R)) is bounded on L(R) for 1 < p <∞. Chanillo (see [2]) proves a similar result when T is replaced by the fractional operators. In [8, 16], Janson and Paluszynski study these results for the Triebel-Lizorkin spaces and the case b ∈ Lipβ(R), where Li...