2021/10/02 by Bhojak, Ankit, Mohanty, Parasar
#42B20 #42B25 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics
paper · doi:10.48550/arxiv.2110.00832
In this paper it is shown that for Ω∈ Llog L(\mathbbSd-1), the rough maximal singular integral operator TΩ^* is of weak type Lloglog L(ℝd). Furthermore, for w∈ A1 and Ω∈ L^∞(\mathbbSd-1), it is shown that TΩ^* is of weak type Lloglog L(w) with weight dependence [w]A1[w]_A∞log([w]_A∞+1), which is same as the best known constant for the singular integral TΩ.