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The minimal operator and the John--Nirenberg theorem for weighted grand Lebesgue spaces

Lihua Peng, Yong Jiao (2015)

Studia Mathematica

We introduce the minimal operator on weighted grand Lebesgue spaces, discuss some weighted norm inequalities and characterize the conditions under which the inequalities hold. We also prove that the John-Nirenberg inequalities in the framework of weighted grand Lebesgue spaces are valid provided that the weight function belongs to the Muckenhoupt A p class.

The monogenic functional calculus

Brian Jefferies, Alan McIntosh, James Picton-Warlow (1999)

Studia Mathematica

A study is made of a symmetric functional calculus for a system of bounded linear operators acting on a Banach space. Finite real linear combinations of the operators have real spectra, but the operators do not necessarily commute with each other. Analytic functions of the operators are formed by using functions taking their values in a Clifford algebra.

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