Landau-type theorem for variable Lebesgue spaces

2016 ◽  
Vol 55 (2) ◽  
Author(s):  
Lech Maligranda ◽  
Witold Wnuk
Keyword(s):  
Type Theorem ◽  
Lebesgue Spaces ◽  
Variable Lebesgue Spaces ◽  
Landau Type Theorem

New variable martingale Hardy spaces

2021 ◽  
pp. 1-29
Author(s):  
Yong Jiao ◽  
Dan Zeng ◽  
Dejian Zhou
Keyword(s):  
Brownian Motion ◽  
Hardy Space ◽  
Hardy Spaces ◽  
Stochastic Integral ◽  
Lebesgue Spaces ◽  
Type Space ◽  
Variable Lebesgue Spaces ◽  
Martingale Inequalities

We investigate various variable martingale Hardy spaces corresponding to variable Lebesgue spaces $\mathcal {L}_{p(\cdot )}$ defined by rearrangement functions. In particular, we show that the dual of martingale variable Hardy space $\mathcal {H}_{p(\cdot )}^{s}$ with $0<p_{-}\leq p_{+}\leq 1$ can be described as a BMO-type space and establish martingale inequalities among these martingale Hardy spaces. Furthermore, we give an application of martingale inequalities in stochastic integral with Brownian motion.

The Calderón operator and the Stieltjes transform on variable Lebesgue spaces with weights

2019 ◽  
Vol 71 (3) ◽  
pp. 443-469
Author(s):  
David Cruz-Uribe ◽  
Estefanía Dalmasso ◽  
Francisco J. Martín-Reyes ◽  
Pedro Ortega Salvador
Keyword(s):  
Stieltjes Transform ◽  
Lebesgue Spaces ◽  
Variable Lebesgue Spaces

Weak-type inequalities and convergence of the ergodic averages in variable Lebesgue spaces with weights

2009 ◽  
Vol 139 (4) ◽  
pp. 673-683 ◽  
Author(s):  
M. Isabel Aguilar Cañestro ◽  
Pedro Ortega Salvador
Keyword(s):  
Lebesgue Space ◽  
Weak Type ◽  
Suitable Condition ◽  
Variable Exponents ◽  
Ergodic Averages ◽  
Lebesgue Spaces ◽  
Variable Lebesgue Spaces ◽  
Almost Everywhere ◽  
Variable Lebesgue Space ◽  
Measure Preserving Transformation

We characterize the weighted weak-type inequalities with variable exponents for the maximal operator associated with an ergodic, invertible, measure-preserving transformation and prove the almost everywhere convergence of the ergodic averages for all functions in a variable Lebesgue space with a weight verifying a suitable condition.

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