The characterization of the Triebel-Lizorkin spaces forp=∞

On the boundedness of pseudo-differential operators on Triebel–Lizorkin and Besov spaces

“…which completes the proof for T (2) . To see (5.5) we apply the size estimate (3.10), but it may not be true when we drop the hypothesis of compact support of a(x, ξ) in x variable.…”

“…Let T (j) be the pseudo-differential operators corresponding to each a (j) . Then our claim is that for any s, m ∈ R and 0 < t ≤ ∞, T (1) and T (2) satisfy the estimates…”

“…This proves (5.3) when i = 1. Now we deal with T (2) . We break up this operator into two parts as (3.8).…”

Continuous Characterization of the Triebel-Lizorkin Spaces and Fourier Multipliers

“…where the second equivalence holds for a sufficiently large λ (as large as stated in p. 544, [3]). A different choice of ϕ from O α yields equivalent quasi-norms in (3.7).…”

“…Based on the work ( [1], [2], [3]) of H. Bui, M. Paluszyński and M. Taibleson, our characterizing means are defined in terms of integrals rather than sums.…”