Capítulos (Análisis Matemático)https://hdl.handle.net/11441/108102019-05-19T22:49:05Z2019-05-19T22:49:05ZA note on the off-diagonal Muckenhoupt-Wheeden conjecturehttps://hdl.handle.net/11441/645382017-09-21T08:01:57Z2016-01-01T00:00:00ZA note on the off-diagonal Muckenhoupt-Wheeden conjecture
Navarro Pascual, Juan Carlos; Kaidi Lhachmi, El Amin
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.
2016-01-01T00:00:00ZIntroduction to hyperconvex spaceshttps://hdl.handle.net/11441/601112017-05-19T09:22:36Z2001-01-01T00:00:00ZIntroduction to hyperconvex spaces
Kirk, William Art; Sims, Brailey
The notion of hyperconvexity is due to Aronszajn and Panitchpakdi (1956) who proved that a hyperconvex space is a nonexpansive absolute retract, i.e. it is a nonexpansive retract of any metric space in which it is isometrically embedded. The corresponding linear theory is well developed and associated with the names of Gleason, Goodner, Kelley and Nachbin (see for instance. The nonlinear theory is still developing. The recent interest into these spaces goes back to the results of Sine and Soardi who proved independently that fixed point property for nonexpansive mappings holds in bounded hyperconvex spaces. Since then many interesting results have been shown to hold in hyperconvex spaces.
2001-01-01T00:00:00ZEl principio de Calderón-Zygmundhttps://hdl.handle.net/11441/482352016-11-29T12:22:39Z2001-01-01T00:00:00ZEl principio de Calderón-Zygmund
Español González, Luis; Varona Malumbres, Juan Luis
In this note we show some estimates for multilinear commutators with vector symbol b = (b1,...,bm) defined by the expression Tbf(x) = Z Rn2 4Ym j=1
(bj (x) − bj (y)) 3 5 K(x, y)f(y) dy, where K is the kernel of any Calderón-Zygmund operator. We generalize and sharpen both classical results from Coifman, and Coifman, Rochberg and Weiss; and also more recent results from the first author. We show that these operators are intimately related to certain appropriate Orlicz type maximal function of the form ML(log L)α where the number α is related to the symbol b.
2001-01-01T00:00:00ZLos q-polinomios hipergeométricoshttps://hdl.handle.net/11441/481742016-11-29T12:22:39Z2001-01-01T00:00:00ZLos q-polinomios hipergeométricos
Español González, Luis; Varona Malumbres, Juan Luis
It is well known that the q-polynomials of hypergeometric type are the polynomial solutions of a certain second order difference equation in a non-uniform lattice. In this short paper we present a modification of the proof of a Theorem by Atakishiyev, Rahman, and Suslov that characterizes the most general lattice.
2001-01-01T00:00:00Z