Abstract
We give necessary and sufficient conditions for a function to be a multiplier from one Besov space B m p (R n)into another B l p (R n)where 0 < l≤ mandp∈ (1, ∞). We also show that the space of multipliers acting from the Sobolev space W m p (R n) into a distribution Sobolev space W −k p (R n )is isomorphic to W −k p, unif (R n) ∩ W −m p, unif (R n) for eitherk > m >0,k > n/p’, or m >k >0, m >n/p, wherepE (1, ∞) andp + p’.= pp’.
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Maz’ya, V., Shaposhnikova, T. (2004). Characterization of Multipliers in Pairs of Besov Spaces. In: Gohberg, I., Wendland, W., Ferreira dos Santos, A., Speck, FO., Teixeira, F.S. (eds) Operator Theoretical Methods and Applications to Mathematical Physics. Operator Theory: Advances and Applications, vol 147. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7926-2_35
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DOI: https://doi.org/10.1007/978-3-0348-7926-2_35
Publisher Name: Birkhäuser, Basel
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Online ISBN: 978-3-0348-7926-2
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