A remark about Calderón-Hardy spaces with variable exponents
Pablo Rocha
Abstract
In this note we improve the parameter $q$ that appears in Theorem 1 obtained by the author in [Math. Ineq. \& appl., Vol 19 (3) (2016), 1013-1030].
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A remark about Calderón-Hardy spaces with variable exponents
Authors
Abstract
In this note we improve the parameter that appears in Theorem 1 obtained by the author in [Math. Ineq. \& appl., Vol 19 (3) (2016), 1013-1030].
Paper Structure
This paper contains 4 theorems, 18 equations.
Key Result
Theorem 1
Let $p(\cdot)$ be an exponent that belongs to $LH_{0}(\mathbb{R}^{n})\cap LH_{\infty}(\mathbb{R}^{n})$, $1 < q < \infty$ and $m \in \mathbb{N}$ such that $0 < p_{-} \leq p_{+} < \infty$ and $n (2m + n/q)^{-1} < \underline{p}$. Then for $q$ sufficiently large the operator $\Delta^{m}$ is a bijective hold for all $F \in \mathcal{H}^{p(\cdot)}_{q, 2m}(\mathbb{R}^{n})$.
Theorems & Definitions (6)
- Theorem 1
- Proposition 2
- proof
- Lemma 3
- proof
- Theorem 4