Bae-Joon Park

Abstract In this work we give some maximal inequalities in Triebel–Lizorkin spaces, which are “ ‐variants” of Fefferman–Stein vector‐valued maximal inequality and Peetre's maximal inequality. We will give some applications of the new maximal inequalities and discuss sharpness of some results.

In this work, we establish sharp boundedness results for pseudo-differential operators corresponding to a ∈ S 0 , 0 m on Triebel–Lizorkin spaces F p s , q and Besov spaces B p s , q .

Abstract We provide an improvement of Calderón and Torchinsky’s version [ 5] of the Hörmander multiplier theorem on Hardy spaces $H^p$ ($0<p<\infty $), substituting the Sobolev space $L_s^2(A_0)$ by the Lorentz–Sobolev space $L_s^{\tau ^{(s,p)},\min (1,p) }(A_0)$, where $\tau ^{(s,p)} =\frac{n}{s-(n/\min{(1,p)}-n)}$ and $A_0$ is the annulus $\{\xi \in{\mathbb{R}}^n:\,\, 1/2<|\xi |<2\}$. Our theorem also extends that of Grafakos and Slavíková [ 10] to the range $0 &amp

Abstract In this work, we obtain the pointwise almost everywhere convergence for two families of multilinear operators: (a) the doubly truncated homogeneous singular integral operators associated with $L^q$ functions on the sphere and (b) lacunary multiplier operators of limited smoothness. The a.e. convergence is deduced from the $L^2\times \cdots \times L^2\to L^{2/m}$ boundedness of the associated maximal multilinear operators.

Pseudo-differential operators of type $(1,1)$ and order $m$ are continuous from $F_p^{s+m,q}$ to $F_p^{s,q}$ if $s \gt d/\!\min{(1,p,q)}-d$ for $0 \lt p \lt \infty$, and from $B_p^{s+m,q}$ to $B_{p}^{s,q}$ if $s \gt d/\!\min{(1,p)}-d$ for $0 \lt p\leq\inf

In this work we give some maximal inequalities in Triebel-Lizorkin spaces, which are "$\dot{F}_{\infty}^{s,q}$-variants" of Fefferman-Stein vector-valued maximal inequality and Peetre's maximal inequality. We will give some applications of the new maximal inequalities and discuss sharpness of some results.

Abstract In this paper, we study sharp maximal function estimates for multilinear pseudo‐differential operators. Our target is operators of type (0,0) for which a differentiation does not make any decay of the associated symbol. Analogous results for operators of type , , appeared in an earlier work of the authors [17], but a different approach is given for .