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We consider operators of the form with Ω(y,u) = K(y,u)h(y-u), where K is a Calderón-Zygmund kernel and (see (0.1) and (0.2)). We give necessary and sufficient conditions for such operators to map the Besov space (= B) into itself. In particular, all operators with , a > 0, a ≠ 1, map B into itself.
2000 Mathematics Subject Classification: 26A33, 33C60, 44A15, 35K55Denoting by Dα0|t the time-fractional derivative of order α (α ∈ (0, 1)) in the sense of Caputo, and by ∆H the Laplacian operator on the (2N + 1) - dimensional Heisenberg group H^N, we prove some nonexistence results for solutions to problems of the type
Dα0|tu − ∆H(au) >= |u|^p,
Dα0|tu − ∆H(au) >= |v|^p,
Dδ0|tv − ∆H(bv) >= |u|^q,
in H^N × R+ , with a, b ∈ L ∞ (H^N × R+).
For α = 1 (and δ = 1 in the case of two inequalities),...
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