Weighted estimates for dyadic paraproducts and t-Haar multipiers with complexity (m,n)

We extend the definitions of dyadic paraproduct and t-Haar multipliers to dyadic operators that depend on the complexity (m,n), for m and n positive integers. We will use the ideas developed by Nazarov and Volberg to prove that the weighted L^2(w)-norm of a paraproduct with complexity (m,n) associated to a function b\in BMO, depends linearly on the A_2-characteristic of the weight w, linearly on the BMO-norm of b, and polynomially in the complexity. This argument provides a new proof of the linear bound for the dyadic paraproduct (the one with complexity (0,0)). Also we prove that the L^2-norm of a t-Haar multiplier for any t and weight w depends on the square root of the C_{2t}-characteristic of w times the square root of the A_2-characteristic of w^{2t} and polynomially in the complexity (m,n), recovering a result of Beznosova for the (0,0)-complexity case.Comment: 27 page

Weighted square function inequalities

For an integrable function f on [0, 1)d, let S(f) and M f denote the corresponding dyadic square function and the dyadic maximal function of f, respectively. The paper contains the proofs of the following statements. (i) If w is a dyadic A1 weight on [0, 1)d, then $l 1(w). The exponent 1/2 is shown to be the best possible. (ii) For any p > 1, there are no constants cp, αp epending only on p such that for all dyadic Ap weights w on [0, 1)d,$l 1(w). $l 1(w) ≤√ 5[w] 1/2 A1$l 1(w) ≤ cp[w] αp Ap $m f$s (f

A new generalization of the Takagi function

We consider a one-parameter family of functions $\{F(t,x)\}_{t}$ on $[0,1]$ and partial derivatives $\partial_{t}^{k} F(t, x)$ with respect to the parameter $t$. Each function of the class is defined by a certain pair of two square matrices of order two. The class includes the Lebesgue singular functions and other singular functions. Our approach to the Takagi function is similar to Hata and Yamaguti. The class of partial derivatives $\partial_{t}^{k} F(t, x)$ includes the original Takagi function and some generalizations. We consider real-analytic properties of $\partial_{t}^{k} F(t, x)$ as a function of $x$, specifically, differentiability, the Hausdorff dimension of the graph, the asymptotic around dyadic rationals, variation, a question of local monotonicity and a modulus of continuity. Our results are extensions of some results for the original Takagi function and some generalizations.Comment: 22 pages, 2 figures. The structure of paper has been changed significantl

ISI Cancellation Using Blind Equalizer Based on DBC Model for MIMO-RFID Reader Reception

Under the dyadic backscatter channel (DBC) model, a conventional zero forcing (ZF) and minimum mean square error (MMSE) method for MIMO-RFID reader reception are not able to be rapidly cancelled inter-symbol interference (ISI) because of the error of postpreamble transmission. In order to achieve the ISI cancellation, the conventional method of ZF and MMSE are proposed to resolve a convergence rate without postpreamble by using a constant modulus algorithm (CMA). Depending on the cost function, the CMA is used which based on second order statistics to estimate the channel statement of channel transfer function. Furthermore, the multiple-tag detection is also considered under the assumption of the maximum likelihood estimation. The comparison of the conventional method and the proposed method is analyzed by using computer simulation and experimental data. We can see that the proposed method is better than the conventional method with a faster ISI cancelling and a lower bit error rate (BER) improving as up to 12 tags