Pseudo-differential Operators with Semi-Quasielliptic Symbols Over p-adic Fields

Hörmander classes of pseudo-differential operators over the compact group of $p$-adic integers

The purpose of this paper is to introduce new definitions of Hörmander classes for pseudo-differential operators over the compact group of $p$-adic integers. Our definitions possess a symbolic calculus, asymptotic expansions and parametrices, together with an interesting relation with the infinite matrices algebras studied by K. Gröchenig and S. Jaffard. Also, we show how our definition of Hörmander classes is related to the definition given in the toroidal case by M. Ruzhansky and V. Turunen. In order to show the special properties of our definition, in a later work, we will study several spe…

Weak And Strong Boundedness For P-adic Fractional Hausdorff Operator And Its Commutator

In this paper, boundedness of Hausdorff operator on weak central Morrey space is obtained. Furthermore, we investigate the weak bounds of p- adic fractional Hausdorff Operator on weighted p-adic weak Lebesgue Space. We also obtain the sufficient condition of commutators of p-adic fractional Hausdorff Operator by taking symbol function from Lipschitz space. Moreover, strong type estimates for fractional Hausdorff Operator and its commutator on weighted p-adic Lorentz space are also acquired.

Weighted Lebesgue and central Morrey estimates for p-adic multilinear Hausdorff operators and its commutators

In this paper, we establish the sharp boundedness of p-adic multilinear Hausdorff operators on the product of Lebesgue and central Morrey spaces associated with both power weights and Muckenhoupt weights. Moreover, the boundedness for the commutators of p-adic multilinear Hausdorff operators on the such spaces with symbols in central BMO space is also obtained.

Some estimates for p-adic rough multilinear Hausdorff operators and commutators on weighted Morrey-Herz type spaces

The aim of this paper is to introduce and study the boundedness of a new class of p-adic rough multilinear Hausdorff operators on the product of Herz, central Morrey and Morrey-Herz spaces with power weights and Muckenhoupt weights. We also establish the boundedness for the commutators of p-adic rough multilinear Hausdorff operators on the weighted spaces with symbols in central BMO space.

一类与数的零冗余s-符号编码相关的Tribin函数

A class of Tribin functions related to $s$-symbol encodings of numbers with a zero redundancy

本文提出了一类与数的零冗余s-符号编码相关的Tribin函数，通过二符号表示与s-符号表示的转换，研究了连续非单调函数的构造与性质。

算子值交换子涉及鞅仿积的有界性

Boundedness of operator-valued commutators involving martingale paraproducts

本文证明了涉及鞅仿积与左乘算子的算子值交换子在非交换$L_p$空间上的有界性，并探讨了半交换鞅仿积基于$BMO$空间的外推性质。