scholarly journals Weighted boundedness of multilinear operator associated to multiplier operator for the extreme cases

2016 ◽  
Vol 17 (1) ◽  
pp. 483
Author(s):  
Jinsong Pan ◽  
Lijuan Tong
Keyword(s):  
Multilinear Operator ◽  
Multiplier Operator

Mean oscillation and boundedness of multilinear operator related to multiplier operator

2021 ◽  
Vol 19 (1) ◽  
pp. 747-759
Author(s):  
Qiaozhen Zhao ◽  
Dejian Huang
Keyword(s):  
Orlicz Spaces ◽  
Multilinear Operator ◽  
Lebesgue Spaces ◽  
Multiplier Operator ◽  
Mean Oscillation

Abstract In this paper, the boundedness of certain multilinear operator related to the multiplier operator from Lebesgue spaces to Orlicz spaces is obtained.

scholarly journals Multilinear operator-valued Calderón-Zygmund theory

2020 ◽  
Vol 279 (8) ◽  
pp. 108666 ◽  
Author(s):  
Francesco Di Plinio ◽  
Kangwei Li ◽  
Henri Martikainen ◽  
Emil Vuorinen
Keyword(s):  
Multilinear Operator

The Riesz potential as a multilinear operator into general BMOβ spaces

2011 ◽  
Vol 173 (6) ◽  
pp. 643-655 ◽  
Author(s):  
H. Aimar ◽  
S. Hartzstein ◽  
B. Iaffei ◽  
B. Viviani
Keyword(s):  
Riesz Potential ◽  
Multilinear Operator

scholarly journals Controlled G-Frames and Their G-Multipliers in Hilbert spaces

2013 ◽  
Vol 21 (2) ◽  
pp. 223-236 ◽  
Author(s):  
Asghar Rahimi ◽  
Abolhassan Fereydooni
Keyword(s):  
Hilbert Spaces ◽  
Iterative Algorithms ◽  
Multiplier Operator ◽  
Frame Operator ◽  
Fixed Sequence ◽  
Numerical Efficiency ◽  
Bessel Sequences ◽  
Almost All

Abstract Multipliers have been recently introduced by P. Balazs as operators for Bessel sequences and frames in Hilbert spaces. These are opera- tors that combine (frame-like) analysis, a multiplication with a fixed sequence ( called the symbol) and synthesis. One of the last extensions of frames is weighted and controlled frames that introduced by P.Balazs, J-P. Antoine and A. Grybos to improve the numerical efficiency of iterative algorithms for inverting the frame operator. Also g-frames are the most popular generalization of frames that include almost all of the frame extensions. In this manuscript the concept of the controlled g- frames will be defined and we will show that controlled g-frames are equivalent to g-frames and so the controlled operators C and C' can be used as preconditions in applications. Also the multiplier operator for this family of operators will be introduced and some of its properties will be shown.

Duals and multipliers of controlled frames in Hilbert spaces

2018 ◽  
Vol 16 (06) ◽  
pp. 1850057 ◽  
Author(s):  
M. Rashidi-Kouchi ◽  
A. Rahimi ◽  
Firdous A. Shah
Keyword(s):  
Hilbert Spaces ◽  
Dual Frames ◽  
Multiplier Operator ◽  
Mild Conditions ◽  
Multiplier Operators ◽  
Approximate Duality

In this paper, we introduce and characterize controlled dual frames in Hilbert spaces. We also investigate the relation between bounds of controlled frames and their related frames. Then, we define the concept of approximate duality for controlled frames in Hilbert spaces. Next, we introduce multiplier operators of controlled frames in Hilbert spaces and investigate some of their properties. Finally, we show that the inverse of a controlled multiplier operator is also a controlled multiplier operator under some mild conditions.

Maximal operators associated to Fourier multipliers with an arbitrary set of parameters

1998 ◽  
Vol 128 (4) ◽  
pp. 683-696 ◽  
Author(s):  
Javier Duoandikoetxea ◽  
Ana Vargas
Keyword(s):  
Convex Body ◽  
Maximal Operator ◽  
The Body ◽  
Fourier Multipliers ◽  
Maximal Operators ◽  
Minkowski Dimension ◽  
Real Numbers ◽  
Positive Real ◽  
Multiplier Operator ◽  
Range Of Values

We present here some general results of boundedness on LP for maximal operators of the form , where E is a subset of the positive real numbers and Tt is a dilation of a fixed multiplier operator. The range of values of p depends only on the decay at infinity of the multiplier and the Minkowski dimension of E. For the case being the maximal operator associated to a convex body, we prove that the norm of the operator is independent of the body.

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