Extrapolation from A∞ weights and applications

We generalize the Ap extrapolation theorem of Rubio de Francia to A∞ weights in the context of Muckenhoupt bases. Our result has several important features. First, it can be used to prove weak endpoint inequalities starting from strong-type inequalities, something which is impossible using the classical result. Second, it provides an alternative to the technique of good-λ inequalities for proving Lp norm inequalities relating operators. Third, it yields vector-valued inequalities without having to use the theory of Banach space valued operators. We give a number of applications to maximal functions, singular integrals, potential operators, commutators, multilinear Calder´on-Zygmund operators, and multiparameter fractional integrals. In particular, we give new proofs, which completely avoid the good-λ inequalities, of Coifman’s inequality relating singular integrals and the maximal operator, of the Fefferman-Stein inequality relating the maximal operator and the sharp maximal operator, and the Muckenhoupt-Wheeden inequality relating the fractional integral operator and the fractional maximal operator.Ministerio de Ciencia y Tecnologí

Sharp two-weight inequalities for singular integrals, with applications to the Hilbert transform and the Sarason conjecture

We prove two-weight norm inequalities for Calderón-Zygmund singular integrals that are sharp for the Hilbert transform and for the Riesz transforms. In addition, we give results for the dyadic square function and for commutators of singular integrals. As an application we give new results for the Sarason conjecture on the product of unbounded Toeplitz operators on Hardy spaces.Stewart Faculty Development Fund (Trinity College)Ministerio de Educación y Cienci

Generalized Hörmander conditions and weighted endpoint estimates

We consider two-weight estimates for singular integral operators and their commutators with bounded mean oscillation functions. Hörmander type conditions in the scale of Orlicz spaces are assumed on the kernels. We prove weighted weak-type estimates for pairs of weights (u, Su) where u is an arbitrary nonnegative function and S is a maximal operator depending on the smoothness of the kernel. We also obtain sufficient conditions on a pair of weights (u, v) for the operators to be bounded from Lp(v) to Lp,∞(u). One-sided singular integrals, as the differential transform operator, are under study. We also provide applications to Fourier multipliers and homogeneous singular integrals.Ministerio de Ciencia y TecnologíaJunta de AndalucíaMinisterio de Educación y CienciaUniversidad Autónoma de Madrid / Comunidad de MadridConsejo Nacional de Investigaciones Científicas y Técnicas (Argentina)Secretaría de Ciencia y Tecnología (Universidad Nacional de Córdoba

Lack of natural weighted estimates for some singular integral operators

Ministerio de Ciencia y TecnologíaDirección General de Investigación Científica y TécnicaDirección General de Enseñanza Superior e Investigación Científic

The boundedness of classical operators on variable L-p spaces

We show that many classical operators in harmonic analysis ---such as maximal operators, singular integrals, commutators and fractional integrals--- are bounded on the variable Lebesgue space $L^{p(\cdot)}$ whenever the Hardy-Littlewood maximal operator is bounded on $L^{p(\cdot)}$. Further, we show that such operators satisfy vector-valued inequalities. We do so by applying the theory of weighted norm inequalities and extrapolation. As applications we prove the Calder\'on-Zygmund inequality for solutions of $\bigtriangleup u=f$ in variable Lebesgue spaces, and prove the Calder\'on extension theorem for variable Sobolev spaces

Event Marketing : Case Study: Trakehner Hengstmarkt

Sammanfattning Idén till detta examensarbete föddes på basis av min arbetspraktik utomlands. Jag arbetade i Tyskland som beridare/hästskötare kombinerat med marknadsföring av dressyrhästar. Examensarbetet omfattar teori om Event Marketing (marknadsföring via evenemang) kombinerat med ridsport. För att göra sammankopplingen tydligare tar examensarbetet upp ett praktiskt exempel i form av det tyska evenemanget Trakehner Hengstmarkt, som innebär stambokföring av avelshingstar samt auktion av sporthästar. Eftersom Tyskland är ett starkt föregångarland inom ridsporten, var jag intresserad av att reda ut vad tyskarna gör för att lyckas så bra som de gör, samt vad Finland eventuellt kunde lära av Tyskland för att utveckla ridsporten i gynnsam riktning.Tiivistelmä Opinnäytetyöni syntyi ulkomaan työharjoittelujaksoni tuloksena. Olin kolme kuukautta Saksassa ratsuttajan/hevosenhoitajan työtehtävissä yhdistettynä markkinointitehtäviin. Tänä aikana kohtasin monia markkinointikeinoja, joista tapahtumamarkkinointi (Event Marketing) teki minuun suurimman vaikutuksen. Koska Saksa on Suomea paljon kehittyneempi ratsujalostuksessa ja ratsastusurheilussa, heräsi kysymys, miksi saksalaiset onnistuvat tässä niin hyvin, ja mitä Suomella olisi opittavaa Saksan käytännöistä. Saksalainen tapahtuma Trakehner Hengstmarkt on tapahtumamarkkinoinnin parhaimpia konkreettisia esimerkkejä, joten olen yhdistänyt teoriaa tapahtumien järjestämisestä markkoinointikeinona ratsujalostukseen sekä ratsastusurheiluun.Summary My bachelor´s thesis is a result of my time as a trainee in Germany. I was working as a rider/groom in combination with marketing dressage horses. While working with marketing of horses I had the opportunity to observe a lot of different types of marketing. I found a high interest in Event Marketing or marketing horses through events. Because Germany is far more developed when it comes to Marketing competition horses, and horse breeding are highly developed in Germany, I wanted to find out why Germany always manages so well, and what could Finland learn to become more successful when it comes to equestrian sports? This thesis is based on theory about event marketing combined with observations about the biggest yearly equestrian event in Germany, Trakehner Hengstmarkt

A note on the off-diagonal Muckenhoupt-Wheeden conjecture

We obtain the off-diagonal Muckenhoupt-Wheeden conjec-ture for Calder´on-Zygmund operators. Namely, given 1 < p < q < ∞ and a pair of weights (u, v), if the Hardy-Littlewood maximal functionsatisfies the following two weight inequalities: M : Lp(v) → Lq(u) and M : Lq´(u1−q´) → Lp´(v1−p´), then any Calderón-Zygmund operator Tand its associated truncatedmaximal operator T⋆ are bounded from Lp(v) to Lq(u). Additionally, as-suming only the second estimate for Mthen Tand T* map continuouslyLp(v) into Lq,∞(u). We also consider the case of generalized Haar shiftoperators and show that their off-diagonal two weight estimates are gov-erned by the corresponding estimates for the dyadic Hardy-Littlewoodmaximal function

Desigualdades con pesos en el Análisis de Fourier: de los espacios de tipo homogéneo a las medidas no doblantes

Tesis doctoral inédita. Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Matemáticas, Fecha de lectura: 25-05-200