BOUNDEDNESS OF g-FUNCTIONS ON TRIEBEL-LIZORKIN SPACES

Triebel-Lizorkin space boundedness of Marcinkiewicz integrals associated to surfaces

“…Theorem A [35]. If Ω ∈ H 1 (S n−1 ) satisfies the cancellation condition (1), then μ Ω is bounded on the inhomogeneous Triebel-Lizorkin space F α p,q (R n ) for 0 < α < 1 and 1 < p, q < ∞.…”

“…There are also papers concerning Triebel-Lizorkin space boundedness of Marcinkiewicz integrals, [35], [36], [38]. We cite the following two.…”

Boundedness and Continuity of Several Integral Operators with Rough Kernels inWFβSn-1Liu1 2018Journal of Function Spaces1020View full textAdd to dashboardCite

“…Suppose that ℎ ∈ Δ (R + ) for some > 1 and Ω ∈ F (S −1 ) for some > max{2, } satisfying (1). Let R , be given as in Theorem 4. (i) Then, for ∈ R and (1/ , 1/ ) ∈ R , , there exists a constant > 0 such that ℎ,Ω,Γ̇, (R ) ≤̇, (R ) (19) for all ∈̇, (R ), where = , , , , , , is independent of the coefficients of { } =1 . (ii) Then, for ∈ R, ∈ (1, ∞), and |1/ − 1/2| < 1/ max{2, } − 1/ , there exists a constant > 0 such that…”

“…The bounds for parametric Marcinkiewicz integrals have been extensively studied by many authors (see [13][14][15], etc.). In recent years, the investigation of boundedness for parametric Marcinkiewicz integral operators on the Triebel-Lizorkin spaces has also attracted the attention of many authors (see [16][17][18][19] for examples). Particularly, Yabuta [18] proved the following result.…”

Integral operators of Marcinkiewicz type on Triebel–Lizorkin spaces

“…Recently, the investigation of boundedness of on Trieble–Lizorkin spaces has attracted the attention of many authors. In 2009, Zhang and Chen established the boundedness of for and under the condition . Later on, they showed that is bounded on for and if for some .…”