TY - JOUR
T1 - On weighted norm inequalities for the Carleson and Walsh–Carleson operator
AU - Plinio, Francesco Di
AU - Lerner, A.
PY - 2014
Y1 - 2014
N2 - We prove $L^p(w)$ bounds for the Carleson operator ${\mathcal C}$, its lacunary version $\mathcal C_{lac}$, and its analogue for the Walsh series $\W$ in terms of the $A_q$ constants $[w]_{A_q}$ for $1\le q\le p$. In particular, we show that, exactly as for the Hilbert transform, $\|{\mathcal C}\|_{L^p(w)}$ is bounded linearly by $[w]_{A_q}$ for $1\le q
AB - We prove $L^p(w)$ bounds for the Carleson operator ${\mathcal C}$, its lacunary version $\mathcal C_{lac}$, and its analogue for the Walsh series $\W$ in terms of the $A_q$ constants $[w]_{A_q}$ for $1\le q\le p$. In particular, we show that, exactly as for the Hilbert transform, $\|{\mathcal C}\|_{L^p(w)}$ is bounded linearly by $[w]_{A_q}$ for $1\le q
UR - http://jlms.oxfordjournals.org/content/90/3/654.short
UR - https://www.mendeley.com/catalogue/f00edf0e-8992-3fea-bd9c-fa70e455609c/
U2 - https://doi.org/10.1112/jlms/jdu049
DO - https://doi.org/10.1112/jlms/jdu049
M3 - Article
SN - 0024-6107
VL - 90
SP - 654
EP - 674
JO - Journal of the London Mathematical Society
JF - Journal of the London Mathematical Society
IS - 3
M1 - 3
ER -