Decomposition Theorems

2020 ◽  
pp. 95-122
Author(s):  
Sergio Macías
Keyword(s):  
Decomposition Theorems

scholarly journals Weak Orlicz–Hardy martingale spaces

2015 ◽  
Vol 26 (08) ◽  
pp. 1550062 ◽  
Author(s):  
Yong Jiao ◽  
Lian Wu ◽  
Lihua Peng
Keyword(s):  
Atomic Decomposition ◽  
Type Inequality ◽  
Sublinear Operator ◽  
Sufficient Condition ◽  
Concave Functions ◽  
Atomic Decompositions ◽  
Stochastic Basis ◽  
Decomposition Theorems

In this paper, several weak Orlicz–Hardy martingale spaces associated with concave functions are introduced, and some weak atomic decomposition theorems for them are established. With the help of weak atomic decompositions, a sufficient condition for a sublinear operator defined on the weak Orlicz–Hardy martingale spaces to be bounded is given. Further, we investigate the duality of weak Orlicz–Hardy martingale spaces and obtain a new John–Nirenberg type inequality when the stochastic basis is regular. These results can be regarded as weak versions of the Orlicz–Hardy martingale spaces due to Miyamoto, Nakai and Sadasue.

scholarly journals Anti-invariant Riemannian submersions from cosymplectic manifolds onto Riemannian manifolds

Filomat ◽  
2015 ◽  
Vol 29 (7) ◽  
pp. 1429-1444 ◽  
Author(s):  
Cengizhan Murathan ◽  
Erken Küpeli
Keyword(s):  
Riemannian Manifolds ◽  
Riemannian Submersion ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Riemannian Submersions ◽  
Totally Geodesic ◽  
Cosymplectic Manifolds ◽  
Necessary And Sufficient ◽  
Decomposition Theorems ◽  
Characteristic Vector Field

We introduce anti-invariant Riemannian submersions from cosymplectic manifolds onto Riemannian manifolds. We survey main results of anti-invariant Riemannian submersions defined on cosymplectic manifolds. We investigate necessary and sufficient condition for an anti-invariant Riemannian submersion to be totally geodesic and harmonic. We give examples of anti-invariant submersions such that characteristic vector field ? is vertical or horizontal. Moreover we give decomposition theorems by using the existence of anti-invariant Riemannian submersions.

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