Rocky Mountain Journal of Mathematics

Atomic decomposition of martingale weighted Lorentz spaces with two-parameter and applications

Maryam Mohsenipour and Ghadir Sadeghi

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We introduce martingale weighted two-parameter Lorentz spaces and establish atomic decomposition theorems. As an application of atomic decomposition we obtain a sufficient condition for sublinear operators defined on martingale weighted Lorentz spaces to be bounded. Moreover, some interpolation properties with a function parameter of those spaces are obtained.

Article information

Rocky Mountain J. Math., Volume 47, Number 3 (2017), 927-945.

First available in Project Euclid: 24 June 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46B70: Interpolation between normed linear spaces [See also 46M35] 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Secondary: 60G42: Martingales with discrete parameter 60G46: Martingales and classical analysis

Lorentz space interpolation two-parameter martingale atomic decomposition


Mohsenipour, Maryam; Sadeghi, Ghadir. Atomic decomposition of martingale weighted Lorentz spaces with two-parameter and applications. Rocky Mountain J. Math. 47 (2017), no. 3, 927--945. doi:10.1216/RMJ-2017-47-3-927.

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