Let Ω ∈ L(logL+)2(Sn−1 × Sm−1) (n, m 2) satisfy some cancellation conditions. We prove the Lp boundedness (1 < p < ∞ ) of the singular integral T f (x1,x2) = p. v. ∫ ∫ Rn×Rm Ω(y1,y ′ 2)h(ρ1(y1),ρ2(y2)) ρα 1 (y1)ρ β 2 (y2) f (x1 − y1,x2 − y2)dy1 dy2, where ρ1 , ρ2 are some metrics which are homogeneous with respect to certain non-isotropic dilations. We also study the above singular integral alo...

We study the L1→L∞-decay estimates for Klein-Gordon equation in Aharonov-Bohm magnetic fields, and further prove Strichartz with critical electromagnetic potentials. The novel ingredients are Schwartz kernels of spectral measure heat propagator Schrödinger operator fields. In particular, we explicitly construct representation resolvent potentials, that kernel fields satisfies Gaussian boundedne...

We prove three results concerning convolution operators and lacunary maximal functions associated to dilates of measures. First we obtain an H to L bound for lacunary maximal operators under a dimensional assumption on the underlying measure and an assumption on an Lp regularity bound for some p > 1. Secondly, we obtain a necessary and sufficient condition for L boundedness of lacunary maximal ...

We investigate the problem of approximating function f in power-type weighted variable exponent Sobolev space Wr,p(.) ?(.) (0,1), (r = 1, 2, ...), by Hardy averaging operator A (f) (x) 1/x ?x0 f(t)dt. If lies ?(.)(0, 1), it is shown that A||(f)?f|| p(.),?(.)?rp(.) ? C ||f(r) p(.),?(.) , where a positive constant. Moreover, we consider boundedness grand Lebesgue spaces Lp(.),? ?(.)(0,1). The suf...

a new definition of boundedness of linear order-homomorphisms (loh)in $l$-topological vector spaces is proposed. the new definition iscompared with the previous one given by fang [the continuity offuzzy linear order-homomorphism, j. fuzzy math. 5 (4) (1997)829$-$838]. in addition, the relationship between boundedness andcontinuity of lohs is discussed. finally, a new uniform boundednessprincipl...

We investigate Fourier multipliers on the compact dual of arbitrary discrete groups. Our main result is a Hörmander-Mihlin multiplier theorem for finite-dimensional cocycles with optimal smoothness condition. We also find Littlewood-Paley type inequalities in group von Neumann algebras, prove Lp estimates for noncommutative Riesz transforms and characterize L∞ → BMO boundedness for radial Fouri...

We establish precise regularity conditions for Lp-boundedness of Fourier multipliers in the group algebra SLn(R). Our main result is inspired by Hörmander–Mikhlin criterion from classical harmonic analysis, although it substantially and necessarily different. Locally, we get sharp growth rates Lie derivatives around singularity nearly optimal regularity. The asymptotics also match Mikhlin formu...

We consider a positive invertible Lamperti operator T with inverse. Our result concerns the averages Ak,n, 0≤k,n∈Z, and ergodic maximal operatorMTf=supk,n≥0⁡|Ak,nf|=supk,n≥0⁡|1k+n+1∑j=−knTjf|, Hilbert transform defined by HTf(x)=limn→∞⁡∑j=1n1j(Tjf(x)−T−jf(x)) power functions Pr,Tf(x)=(∑n=0∞|An+1,0f(x)−An,0f(x)|r+|A0,n+1f(x)−A0,nf(x)|r)1/r, for 1<r<+∞. Several authors proved that if are uniforml...

which is the Bochner-Riesz operator (see [8]). Let E be the space E = {h : ‖h‖ = supr>0 |h(r)| <∞}, then, for each fixed x ∈ Rn, Bδ r ( f )(x) may be viewed as a mapping from [0,+∞) to E, and it is clear that Bδ ∗( f )(x) = ‖Bδ r ( f )(x)‖ and B ∗,b( f )(x) = ‖b(x)Bδ r ( f )(x)−Bδ r (b f )(x)‖. As well known, a classical result of Coifman et al. [4] proved that the commutator [b,T] generated by...

This article deals with a 2 ? reaction-diffusion-taxis model consisting of Michaelis-Menten functional response predator-prey system. The critical section this is that temporal-spatial evolution the predators? velocity depends largely on gradient prey. But beyond that, system also inscribes prey-taxis mechanism an immediate movement predator u in to change prey v (which leads collection u). By ...