Weighted inequalities for Schrödinger type Singular Integrals on variable Lebesgue spaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929406596874240 |
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| author | Cabral, Adrián |
| author_facet | Cabral, Adrián |
| contents | In this paper we study the boundedness in weighted variable Lebesgue spaces of operators associated with the semigroup generated by the time-independent Schrödinger operator $\mathcal{L}=-Δ+V$ in $\mathbb{R}^d$, where $d>2$ and the non-negative potential $V$ belongs to the reverse Hölder class $RH_q$ with $q>d/2$. Each of the operators that we are going to deal with are singular integrals given by a kernel $K(x,y)$, which satisfies certain size and smoothness conditions in relation to a critical radius function $ρ$ which comes appears naturally in the harmonic analysis related to Schrödinger operator $\mathcal{L}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_04010 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weighted inequalities for Schrödinger type Singular Integrals on variable Lebesgue spaces Cabral, Adrián Analysis of PDEs Primary: 42B20, 42B35, Secondary: 35J10 In this paper we study the boundedness in weighted variable Lebesgue spaces of operators associated with the semigroup generated by the time-independent Schrödinger operator $\mathcal{L}=-Δ+V$ in $\mathbb{R}^d$, where $d>2$ and the non-negative potential $V$ belongs to the reverse Hölder class $RH_q$ with $q>d/2$. Each of the operators that we are going to deal with are singular integrals given by a kernel $K(x,y)$, which satisfies certain size and smoothness conditions in relation to a critical radius function $ρ$ which comes appears naturally in the harmonic analysis related to Schrödinger operator $\mathcal{L}$. |
| title | Weighted inequalities for Schrödinger type Singular Integrals on variable Lebesgue spaces |
| topic | Analysis of PDEs Primary: 42B20, 42B35, Secondary: 35J10 |
| url | https://arxiv.org/abs/2401.04010 |