Weighted weak modular and norm inequalities for the Hardy operator in variable L p spaces of monotone functions

2011 ◽  
Vol 25 (2) ◽  
pp. 459-474 ◽  
Author(s):  
Santiago Boza ◽  
Javier Soria
Keyword(s):  
Hardy Operator ◽  
Monotone Functions ◽  
Norm Inequalities

scholarly journals Embeddings for monotone functions and $B_p$ weights, between discrete and continuous

2005 ◽  
Vol 97 (2) ◽  
pp. 281
Author(s):  
Josep L. Garcia-Domingo
Keyword(s):  
Hardy Operator ◽  
Monotone Functions ◽  
Lebesgue Spaces ◽  
Weighted Lebesgue Spaces ◽  
Monotone Sequences ◽  
Classical Operator ◽  
Continuous Setting

We characterize the embedding for general weighted Lebesgue spaces of monotone functions by using the analog embedding for discrete monotone sequences indexed over the integers. We then use these results to obtain the boundedness of the discrete Hardy operator and to study the connections with the Hardy classical operator in the continuous setting.

scholarly journals Hardy operator with variable limits on monotone functions

2003 ◽  
Vol 1 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Vladimir D. Stepanov ◽  
Elena P. Ushakova
Keyword(s):  
Hardy Operator ◽  
Monotone Functions
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