quasiconcave function
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2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Irshaad Ahmed ◽  
Waqas Nazeer

The optimal couples of rearrangement invariant spaces for boundedness of a generalized maximal operator, associated with a quasiconcave function, have been characterized in terms of certain indices connected with rearrangement invariant spaces and quasiconcave functions.


2006 ◽  
Vol 4 (3) ◽  
pp. 275-304 ◽  
Author(s):  
Evgeniy Pustylnik ◽  
Teresa Signes

We study weak type interpolation for ultrasymmetric spacesL?,Ei.e., having the norm??(t)f*(t)?E˜, where?(t)is any quasiconcave function andE˜is arbitrary rearrangement-invariant space with respect to the measuredt/t. When spacesL?,Eare not “too close” to the endpoint spaces of interpolation (in the sense of Boyd), the optimal interpolation theorem was stated in [13]. The case of “too close” spaces was studied in [15] with results which are optimal, but only among ultrasymmetric spaces. In this paper we find better interpolation results, involving new types of rearrangement-invariant spaces,A?,b,EandB?,b,E, which are described and investigated in detail.


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