Sharp multiplier theorem for multidimensional Bessel operators
| Autor: | Edyta Kania, Marcin Preisner |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Applied Mathematics
General Mathematics 010102 general mathematics 020206 networking & telecommunications 02 engineering and technology Hardy space 01 natural sciences Functional Analysis (math.FA) Combinatorics Multiplier (Fourier analysis) Mathematics - Functional Analysis symbols.namesake Operator (computer programming) 0202 electrical engineering electronic engineering information engineering symbols FOS: Mathematics 42B15 (primary) 42B30 42B20 42B25 (secondary) 0101 mathematics Analysis Bessel function Mathematics |
| Popis: | Consider the multidimensional Bessel operator $$\begin{aligned} B f(x) = -\sum _{j=1}^N \left( \partial _j^2 f(x) +\frac{\alpha _j}{x_j} \partial _j f(x) \right) , \quad x\in (0,\infty )^N. \end{aligned}$$ Let $$d = \sum _{j=1}^N \max (1,\alpha _j+1)$$ be the dimension of the space $$(0,\infty )^N$$ equipped with the measure $$x_1^{\alpha _1}\ldots x_N^{\alpha _N} dx_1\ldots dx_N$$ . In the general case $$\alpha _1,\ldots ,\alpha _N >-1$$ we prove multiplier theorems for spectral multipliers m(B) on $$L^{1,\infty }$$ and the Hardy space $$H^1$$ . We assume that m satisfies the classical Hormander condition $$\begin{aligned} \sup _{t>0} \left\| \eta (\cdot ) m(t\cdot ) \right\| _{W^{2,\beta }(\mathbb {R})} d/2$$ . Furthermore, we investigate imaginary powers $$B^{ib}$$ , $$b\in \mathbb {R}$$ , and prove some lower estimates on $$L^{1,\infty }$$ and $$L^p$$ , $$1 |
| Databáze: | OpenAIRE |
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