
We consider operators of the form: ∫ − ∞ ∞ F t φ ( t ) d t \int _{ - \infty }^\infty {{F_t}\varphi (t)\;dt} , where F t {F_t} is a 1 1 -parameter family of Fourier integral operators and φ ( t ) d t \varphi (t)\;dt a tempered distribution on the real line and show that these operators are sums of pseudo-differential and Fourier integral operators. Here, we give the typical case where φ ( t ) d t = p . v . { 1 / t } \varphi (t)\;dt = {\text {p}}.{\text {v}}.\left \{ {1/t} \right \} . An application to singular integrals on variable curves is given.
Harmonic analysis in several variables, singular integrals on variable curves, Fourier integral operators, Pseudodifferential operators as generalizations of partial differential operators, tempered distribution
Harmonic analysis in several variables, singular integrals on variable curves, Fourier integral operators, Pseudodifferential operators as generalizations of partial differential operators, tempered distribution
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