Remarks on the smoothing effect of the heat semigroup on Ḃsp,∞ (Rn)
We consider the heat semigroup etΔ:Ḃp,∞s(Rn)→Ḃp,∞s(Rn) for 1≤p≤∞ and s∈R. We show that etΔf∈BC((0,∞);Ḃp,∞s(Rn)) for all f∈Ḃp,∞s(Rn). In addition, we reveal a sufficient condition of f∈Ḃp,∞s(Rn) for ensuring the C0-property etΔf∈BC([0,∞);Ḃp,∞s(Rn)). We also give examples of f∈Ḃp,∞s(Rn) which h...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-06-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124001049 |