Weighted mixed-norm inequality on Doob’s maximal operator and John–Nirenberg inequalities in Banach function spaces

2018 ◽  
Vol 157 (2) ◽  
pp. 408-433 ◽  
Author(s):  
W. Chen ◽  
K.-P. Ho ◽  
Y. Jiao ◽  
D. Zhou
Keyword(s):  
Maximal Operator ◽  
Function Spaces ◽  
Norm Inequality ◽  
Mixed Norm ◽  
Banach Function Spaces

scholarly journals Sparse domination implies vector-valued sparse domination

2022 ◽  
Author(s):  
Emiel Lorist ◽  
Zoe Nieraeth
Keyword(s):  
Function Space ◽  
Hilbert Transform ◽  
Maximal Operator ◽  
Banach Function Space ◽  
Orlicz Spaces ◽  
Function Spaces ◽  
Banach Function Spaces ◽  
Bilinear Hilbert Transform ◽  
Vector Valued ◽  
Littlewood Maximal Operator

AbstractWe prove that scalar-valued sparse domination of a multilinear operator implies vector-valued sparse domination for tuples of quasi-Banach function spaces, for which we introduce a multilinear analogue of the $${{\,\mathrm{UMD}\,}}$$ UMD condition. This condition is characterized by the boundedness of the multisublinear Hardy-Littlewood maximal operator and goes beyond examples in which a $${{\,\mathrm{UMD}\,}}$$ UMD condition is assumed on each individual space and includes e.g. iterated Lebesgue, Lorentz, and Orlicz spaces. Our method allows us to obtain sharp vector-valued weighted bounds directly from scalar-valued sparse domination, without the use of a Rubio de Francia type extrapolation result. We apply our result to obtain new vector-valued bounds for multilinear Calderón-Zygmund operators as well as recover the old ones with a new sharp weighted bound. Moreover, in the Banach function space setting we improve upon recent vector-valued bounds for the bilinear Hilbert transform.

scholarly journals The John–Nirenberg inequality in ball Banach function spaces and application to characterization of BMO

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Mitsuo Izuki ◽  
Takahiro Noi ◽  
Yoshihiro Sawano
Keyword(s):  
Maximal Operator ◽  
Function Spaces ◽  
Bounded Mean Oscillation ◽  
Banach Function Spaces ◽  
Mean Oscillation ◽  
Nirenberg Inequality ◽  
Associate Space ◽  
Littlewood Maximal Operator

Abstract Our goal is to obtain the John–Nirenberg inequality for ball Banach function spaces X, provided that the Hardy–Littlewood maximal operator M is bounded on the associate space $X'$ X ′ by using the extrapolation. As an application we characterize BMO, the bounded mean oscillation, via the norm of X.

scholarly journals Non-commutative Banach function spaces

1989 ◽  
Vol 201 (4) ◽  
pp. 583-597 ◽  
Author(s):  
Peter G. Dodds ◽  
Theresa K. -Y. Dodds ◽  
Ben de Pagter
Keyword(s):  
Function Spaces ◽  
Banach Function Spaces

scholarly journals The weak topology on q-convex Banach function spaces

2011 ◽  
Vol 285 (2-3) ◽  
pp. 136-149 ◽  
Author(s):  
L. Agud ◽  
J. M. Calabuig ◽  
E. A. Sánchez Pérez
Keyword(s):  
Weak Topology ◽  
Function Spaces ◽  
Banach Function Spaces

scholarly journals Symmetrization, factorization and arithmetic of quasi-Banach function spaces

2019 ◽  
Vol 470 (2) ◽  
pp. 1136-1166 ◽  
Author(s):  
Paweł Kolwicz ◽  
Karol Leśnik ◽  
Lech Maligranda
Keyword(s):  
Function Spaces ◽  
Banach Function Spaces
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