Abstract. The following subexponential estimate for commutators is provedwhere c and α are absolute constants, T is a Calderón-Zygmund operator, M is the Hardy Littlewood maximal function and f is any function supported on the cube Q ⊂ R n . We also obtain thatwhere m f (Q) is the median value of f on the cube Q and M # λn;Q is Strömberg's local sharp maximal function with λn = 2 −n−2 . As a consequence we derive Karagulyan's estimate:

For any Calderón-Zygmund operator T and any BM O function b we prove the following quadratic estimatewith constant c = c(n, T ) being the estimate optimal on p and the exponent of the weight constant. As an endpoint estimate we provewhich was used to derive vector-valued extensions of the classical estimates for M.1991 Mathematics Subject Classification. Primary 42B20, 42B25. Secondary 46B70, 47B38.

Organizations require their business processes goals and the underlying information technology (IT) to be in synchronization with each other, but the continual changes in business processes makes this difficult. To accomplish this synchronization, there needs to be an alignment between the business processes and the IT. Business processes are currently defined using such well-known notations as BPMN, and the IT is made available by different services. Hence, the alignment process can be defined as one between the organization's BPMNs and the services provided by its IT. In practice, however, this process is a complex task which is carried out by hand and hence is error prone. The present communication analyzes the conditions, relations, and incompatibilities between BPMNs and the service descriptions. The incompatibilities are formalized mathematically in order to facilitate their identification and resolution. Then, an alignment process is defined taking into account these incompatibilities and their solutions. The wrapper code needed to resolve each incompatibility identified during the alignment process is generated automatically. Finally, a case study is presented to validate and illustrate the use of the proposed alignment process. The results provided by the semiautomatic alignment process were similar to those obtained manually by a group of experts. INDEX TERMS Alignment process support, business process alignment, service-oriented architecture, semantic algorithms, service incompatibility resolution. ENCARNA SOSA-SÁNCHEZ received the B.Sc. and Ph.D. degrees in computer science from the University of Granada, in 1995 and 2018, respectively. She is currently pursuing the Ph.D. degree with the Computer Science Department, University of Extremadura, Spain. She is also an Assistant Professor with the Computer Science Department, University of Extremadura. She has published several peer-reviewed papers in international journals, workshops, and conferences. She is involved in several research projects. Her research interests include service-oriented architectures, business process modeling, and model-driven development.

A smart water network consists of a large number of devices that measure a wide range of parameters present in distribution networks in an automatic and continuous way. Among these data, you can find the flow, pressure, or totalizer measurements that, when processed with appropriate algorithms, allow for leakage detection at an early stage. These algorithms are mainly based on water demand forecasting. Different approaches for the prediction of water demand are available in the literature. Although they present successful results at different levels, they have two main drawbacks: the inclusion of several seasonalities is quite cumbersome, and the fitting horizons are not very large. With the aim of solving these problems, we present the application of pattern similarity-based techniques to the water demand forecasting problem. The use of these techniques removes the need to determine the annual seasonality and, at the same time, extends the horizon of prediction to 24 h. The algorithm has been tested in the context of a real project for the detection and location of leaks at an early stage by means of demand forecasting, and good results were obtained, which are also presented in this paper.