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In this paper we study new $$L^p$$Lp–boundedness properties for the integral transform with complex Gaussian kernel over $$L^p ({\mathbb {R}},(1+x^2)^{\alpha } dx)$$Lp(R,(1+x2)αdx), $$1\le p \le \infty $$1≤p≤∞, $$\alpha \in {\mathbb… Click to show full abstract
In this paper we study new $$L^p$$Lp–boundedness properties for the integral transform with complex Gaussian kernel over $$L^p ({\mathbb {R}},(1+x^2)^{\alpha } dx)$$Lp(R,(1+x2)αdx), $$1\le p \le \infty $$1≤p≤∞, $$\alpha \in {\mathbb {R}}$$α∈R. We also obtain Parseval-type relations over these spaces. The Gauss–Weierstrass semigroup on $${\mathbb {R}}$$R is analyzed as a particular case.
Keywords:
operators complex;
type relations;
parseval type;
inequalities operators;
relations inequalities;
complex gaussian
Journal Title: Complex Analysis and Operator Theory
Year Published: 2017
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Journal Title: Complex Analysis and Operator Theory
Year Published: 2017
Link to full text (if available)
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recommendations!