The Hardy space H^1_{FIO}(R^n) for Fourier integral operators equals its Littlewood-Paley g-function, maximal-function, and G*_alpha versions for alpha > 2, with equivalent norms.
Off-singularity bounds and Hardy spaces for Fourier integral operators
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We define a scale of Hardy spaces $\mathcal{H}^{p}_{FIO}(\mathbb{R}^{n})$, $p\in[1,\infty]$, that are invariant under suitable Fourier integral operators of order zero. This builds on work by Smith for $p=1$. We also introduce a notion of off-singularity decay for kernels on the cosphere bundle of $\mathbb{R}^{n}$, and we combine this with wave packet transforms and tent spaces over the cosphere bundle to develop a full Hardy space theory for oscillatory integral operators. In the process we extend the known results about $L^{p}$-boundedness of Fourier integral operators, from local boundedness to global boundedness for a larger class of symbols.
fields
math.AP 1years
2019 1verdicts
ACCEPT 1representative citing papers
citing papers explorer
-
Characterizations of the Hardy space $\mathcal{H}_{FIO}^{1}(\mathbb{R}^{n})$ for Fourier integral operators
The Hardy space H^1_{FIO}(R^n) for Fourier integral operators equals its Littlewood-Paley g-function, maximal-function, and G*_alpha versions for alpha > 2, with equivalent norms.