Browsing by Author "Li, K."
Now showing items 119 of 19

Bilinear CalderónZygmund theory on product spaces
Li, K.; Martikainen, H.; Vuorinen, E. (201910)We develop a wide general theory of bilinear biparameter singular integrals $T$. This includes general Calder\'onZygmund type principles in the bilinear biparameter setting: easier bounds, like estimates in the Banach ... 
Bilinear representation theorem
Li, K.; Martikainen, H.; Ou, Y.; Vuorinen, E. (20180101)We represent a general bilinear CalderónZygmund operator as a sum of simple dyadic operators. The appearing dyadic operators also admit a simple proof of a sparse bound. In particular, the representation implies a so ... 
Bloom type inequality for biparameter singular integrals: efficient proof and iterated commutators
Li, K.; Martikainen, H.; Vuorinen, E. (20190314)Utilising some recent ideas from our bilinear biparameter theory, we give an efficient proof of a twoweight Bloom type inequality for iterated commutators of linear biparameter singular integrals. We prove that if $T$ ... 
Bloom type upper bounds in the product BMO setting
Li, K.; Martikainen, H.; Vuorinen, E. (20190408)We prove some Bloom type estimates in the product BMO setting. More specifically, for a bounded singular integral $T_n$ in $\mathbb R^n$ and a bounded singular integral $T_m$ in $\mathbb R^m$ we prove that $$ \ [T_n^1, ... 
A characterization of two weight norm inequality for LittlewoodPaley $g_{\lambda}^{*}$function
Cao, M.; Li, K.; Xue, Q. (2017)Let $n\ge 2$ and $g_{\lambda}^{*}$ be the wellknown high dimensional LittlewoodPaley function which was defined and studied by E. M. Stein, $$g_{\lambda}^{*}(f)(x)=\bigg(\iint_{\mathbb R^{n+1}_{+}} \Big(\frac{t}{t+xy ... 
Endpoint estimates, extrapolation for multilinear muckenhoupt classes, and applications
Li, K.; Martell, J.M.; Martikainen, H.; Ombrosi, S.; Vuorinen, E. (2019)In this paper we present the results announced in the recent work by the first, second, and fourth authors of the current paper concerning Rubio de Francia extrapolation for the socalled multilinear Muckenhoupt classes. ... 
Flow with $A_\infty(\mathbb R)$ density and transport equation in $\mathrm{BMO}(\mathbb R)$
Jiang, R.; Li, K.; Xiao, J. (201911)We show that, if $b\in L^1(0,T;L^1_{\rm {loc}}(\mathbb R))$ has spatial derivative in the JohnNirenberg space ${\rm{BMO}}(\mathbb R)$, then it generates a unique flow $\phi(t,\cdot)$ which has an $A_\infty(\mathbb R)$ ... 
Multilinear operatorvalued calderónzygmund theory
Di Plinio, F.; Li, K.; Martikainen, H.; Vuorinen, E. (2020)We develop a general theory of multilinear singular integrals with operator valued kernels, acting on tuples of UMD Banach spaces. This, in particular, involves investigating multilinear variants of the Rboundedness ... 
Multilinear singular integrals on noncommutative lp spaces
Di Plinio, F.; Li, K.; Martikainen, H.; Vuorinen, E. (2019)We prove Lp bounds for the extensions of standard multilinear Calderón Zygmund operators to tuples of UMD spaces tied by a natural product structure. The product can, for instance, mean the pointwise product in UMD ... 
New bounds for bilinear CalderónZygmund operators and applications
Damián, W.; Hormozi, M.; Li, K. (20161125)In this work we extend Lacey’s domination theorem to prove the pointwise control of bilinear Calderón–Zygmund operators with Dini–continuous kernel by sparse operators. The precise bounds are carefully tracked following ... 
Proof of an extension of E. Sawyer's conjecture about weighted mixed weaktype estimates
Li, K.; Ombrosi, S.; Pérez, C. (201809)We show that if $v\in A_\infty$ and $u\in A_1$, then there is a constant $c$ depending on the $A_1$ constant of $u$ and the $A_{\infty}$ constant of $v$ such that $$\Big\\frac{ T(fv)} {v}\Big\_{L^{1,\infty}(uv)}\le c\, ... 
RESTRICTED TESTING FOR POSITIVE OPERATORS
Hytönen, T.; Li, K.; Sawyer, E. (2020)We prove that for certain positive operators T, such as the HardyLittlewood maximal function and fractional integrals, there is a constant D>1, depending only on the dimension n, such that the two weight norm inequality ... 
Sharp weighted estimates involving one supremum
Li, K. (201707)In this note, we study the sharp weighted estimate involving one supremum. In particular, we give a positive answer to an open question raised by Lerner and Moen. We also extend the result to rough homogeneous singular ... 
Sparse bounds for maximal rough singular integrals via the Fourier transform
Di Plinio, F.; Hytönen, T.; Li, K. (20190312)We prove a quantified sparse bound for the maximal truncations of convolutiontype singular integrals with suitable Fourier decay of the kernel. Our result extends the sparse domination principle by CondeAlonso, Culiuc, ... 
Sparse domination theorem for multilinear singular integral operators with $L^{r}$Hörmander condition
Li, K. (20170401)In this note, we show that if $T$ is a multilinear singular integral operator associated with a kernel satisfies the socalled multilinear $L^{r}$Hörmander condition, then $T$ can be dominated by multilinear sparse operators. 
Vectorvalued operators, optimal weighted estimates and the $C_p$ condition
Cejas, M.E.; Li, K.; Pérez, C.; RiveraRíos, I.P. (201809)In this paper some new results concerning the $C_p$ classes introduced by Muckenhoupt and later extended by Sawyer, are provided. In particular we extend the result to the full range expected $p>0$, to the weak norm, to ... 
Weak and strong $A_p$$A_\infty$ estimates for square functions and related operators
Hytönen, T.; Li, K. (201707)We prove sharp weak and strong type weighted estimates for a class of dyadic operators that includes majorants of both standard singular integrals and square functions. Our main new result is the optimal bound $[w]_{A_p} ... 
Weighted mixed weaktype inequalities for multilinear operators
Li, K.; Ombrosi, S.; Picardi, B. (2017)In this paper we present a theorem that generalizes Sawyer's classic result about mixed weighted inequalities to the multilinear context. Let $\vec{w}=(w_1,...,w_m)$ and $\nu = w_1^\frac{1}{m}...w_m^\frac{1}{m}$, the main ... 
Weighted norm inequalities for rough singular integral operators
Li, K.; Pérez, C.; RiveraRíos, I.P.; Roncal, L. (20180817)In this paper we provide weighted estimates for rough operators, including rough homogeneous singular integrals $T_\Omega$ with $\Omega\in L^\infty(\mathbb{S}^{n1})$ and the BochnerRiesz multiplier at the critical index ...