scholarly journals Almost everything you need to know about relatively compact sets in variable Lebesgue spaces

2015 ◽  
Vol 269 (7) ◽  
pp. 1925-1949 ◽  
Author(s):  
Przemysław Górka ◽  
Anna Macios
Keyword(s):  
Compact Sets ◽  
Lebesgue Spaces ◽  
Variable Lebesgue Spaces

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.

scholarly journals Fréchet Envelopes of Nonlocally Convex Variable Exponent Hörmander Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Joaquín Motos ◽  
María Jesús Planells ◽  
César F. Talavera
Keyword(s):  
Analytic Functions ◽  
Maximal Operator ◽  
Variable Exponent ◽  
Previous Article ◽  
Lebesgue Spaces ◽  
Variable Lebesgue Spaces ◽  
Complemented Subspace ◽  
Open Set ◽  
Hörmander Spaces ◽  
Littlewood Maximal Operator

We show that the dual Bp·locΩ′ of the variable exponent Hörmander space Bp(·)loc(Ω) is isomorphic to the Hörmander space B∞c(Ω) (when the exponent p(·) satisfies the conditions 0<p-≤p+≤1, the Hardy-Littlewood maximal operator M is bounded on Lp(·)/p0 for some 0<p0<p- and Ω is an open set in Rn) and that the Fréchet envelope of Bp(·)loc(Ω) is the space B1loc(Ω). Our proofs rely heavily on the properties of the Banach envelopes of the p0-Banach local spaces of Bp(·)loc(Ω) and on the inequalities established in the extrapolation theorems in variable Lebesgue spaces of entire analytic functions obtained in a previous article. Other results for p(·)≡p, 0<p<1, are also given (e.g., all quasi-Banach subspace of Bploc(Ω) is isomorphic to a subspace of lp, or l∞ is not isomorphic to a complemented subspace of the Shapiro space hp-). Finally, some questions are proposed.

Variable Lebesgue Spaces

2013 ◽  
Author(s):  
David V. Cruz-Uribe ◽  
Alberto Fiorenza
Keyword(s):  
Lebesgue Spaces ◽  
Variable Lebesgue Spaces
Sign in / Sign up

Export Citation Format

Share Document