POINTWISE CONVERGENCE AND SEMIGROUPS ACTING ON VECTOR-VALUED FUNCTIONS
2011 ◽
Vol 84
(1)
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pp. 44-48
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Keyword(s):
AbstractA submarkovian C0 semigroup (Tt)t∈ℝ+ acting on the scale of complex-valued functions Lp(X,ℂ) extends to a semigroup of operators on the scale of vector-valued function spaces Lp(X,E), when E is a Banach space. It is known that, if f∈Lp(X,ℂ), where 1<p<∞, then Ttf→f pointwise almost everywhere. We show that the same holds when f∈Lp(X,E) .
1996 ◽
Vol 39
(3)
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pp. 485-490
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Keyword(s):
1989 ◽
Vol 41
(4)
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pp. 659-675
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Keyword(s):
1987 ◽
Vol 101
(1)
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pp. 107-112
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1996 ◽
Vol 124
(2)
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pp. 324-342
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Keyword(s):
1988 ◽
Vol 40
(3)
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pp. 610-632
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Keyword(s):
2018 ◽
Vol 25
(2)
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pp. 561-580
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Keyword(s):
1972 ◽
Vol 167
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pp. 263-263
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