Weighted and endpoint estimates for commutators of bilinear pseudo-differential operators

<abstract><p>In this paper, by applying the accurate estimates of the Hörmander class, the authors consider the commutators of bilinear pseudo-differential operators and the operation of multiplication by a Lipschitz function. By establishing the pointwise estimates of the corresponding sharp maximal function, the boundedness of the commutators is obtained respectively on the products of weighted Lebesgue spaces and variable exponent Lebesgue spaces with $ \sigma \in\mathcal{B}BS_{1, 1}^{1} $. Moreover, the endpoint estimate of the commutators is also established on $ L^{\infty}\times L^{\infty} $.</p></abstract>

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.

Uniform estimates with data from generalized Lebesgue spaces in periodic structures

We study various types of uniform Calderón–Zygmund estimates for weak solutions to elliptic equations in periodic homogenization. A global regularity is obtained with respect to the nonhomogeneous term from weighted Lebesgue spaces, Orlicz spaces, and weighted Orlicz spaces, which are generalized Lebesgue spaces, provided that the coefficients have small BMO seminorms and the domains are δ-Reifenberg domains.

Approximation theorems in weighted Lebesgue spaces with variable exponent

In this work, approximation properties of de la Vall?e-Poussin means are investigated in weighted Lebesgue spaces with variable exponent where weight function belongs to Muckenhoupt class. For this purpose direct, inverse and simultaneous theorems of approximation theory are proved and constructive characterizations of functions are obtained in weighted Lebesgue spaces with variable exponent.

Boundedness of multilinear Calderón-Zygmund singular operators on weighted Lebesgue spaces and Morrey-Herz spaces with variable exponents

<abstract><p>In this paper, we introduce weighted Morrey-Herz spaces $ M\dot K^{\alpha, \lambda}_{q, p(\cdot)}(w~^{p(\cdot)}) $ with variable exponent $ p(\cdot) $. Then we prove the boundedness of multilinear Calderón-Zygmund singular operators on weighted Lebesgue spaces and weighted Morrey-Herz spaces with variable exponents.</p></abstract>

Boundedness of vector-valued sublinear operators on weighted Herz-Morrey spaces with variable exponents

If vector-valued sublinear operators satisfy the size condition and the vector-valued inequality on weighted Lebesgue spaces with variable exponent, then we obtain their boundedness on weighted Herz-Morrey spaces with variable exponents.