Weak (1,1) bounded operators
We construct a class of Fourier multipliers whose associated operators are weak (1,1) bounded but fail to be weak (p, p) bounded for any 1 < p \leq \infty. Moreover, we show that this result is sharp.
math.FA↗
arXiv subjects
Arup Maity
Publications and source records attributed to Arup Maity.
A note on Singular integral
In this paper, we prove that for $\frac{n}{2}+\frac{1}{4}<α\leq\frac{n+1}{2} $, the convolution operator $$S_α f(x)=\int_{|y| \geq 1} f(x-y)\left(|y|^{2}-1\right)^{-α} d y$$ is bounded from $L^p$ to $L^q$ for certain values of $p$ and $q$.
math.CA↗