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Lipschitz algebras and Lipschitz-Free spaces over unbounded metric spaces
(Oxford University Press, 2021)
Artículo / Artikulua,
We investigate a way to turn an arbitrary (usually, unbounded) metric space M into a bounded metric space B in such a way that the corresponding Lipschitz-free spaces F(M) and F(B) are isomorphic. The construction we provide ...
Structure of the Lipschitz free p-spaces Fp(Zd) and Fp(Rd) for 0 < p ≤ 1
(Springer, 2021)
info:eu-repo/semantics/article,
Our aim in this article is to contribute to the theory of Lipschitz free p-spaces for 0 < p ≤ 1 over the Euclidean spaces Rd and Zd. To that end, on one hand we show that Fp(Rd) admits a Schauder basis for every p ∈ 2 (0, ...
Lipschitz free spaces isomorphic to their infinite sums and geometric applications
(American Mathematical Society, 2021)
info:eu-repo/semantics/article,
We find general conditions under which Lipschitz-free spaces over metric spaces are isomorphic to their infinite direct _1-sum and exhibit several applications. As examples of such applications we have that Lipschitz-free ...
Democracy of quasi-greedy bases in p-Banach spaces with applications to the efficiency of the thresholding greedy algorithm in the hardy spaces Hp(Dd)
(Cambridge University Press, 2023)
Artículo / Artikulua,
We use new methods, specific for non-locally convex quasi-Banach spaces, to investigate when the quasi-greedy bases of a -Banach space for 0 < p < p are democratic. The novel techniques we obtain permit to show in particular ...
Unconditional and quasi-greedy bases in L-p with applications to Jacobi polynomials Fourier series
(European Mathematical Society, 2019)
info:eu-repo/semantics/article,
We show that the decreasing rearrangement of the Fourier series with respect to the Jacobi polynomials for functions in L-p does not converge unless p = 2. As a by-product of our work on quasi-greedy bases in L-p(µ), we ...
Building highly conditional almost greedy and quasi-greedy bases in Banach spaces
(Elsevier, 2019)
info:eu-repo/semantics/article,
It is known that for a conditional quasi-greedy basis B in a Banach space X, the associated sequence (k(m)[B](m=1)(infinity) of its conditionality constants verifies the estimate k(m)[B] = O(log m) and that if the reverse ...
Asymptotic greediness of the Haar system in the spaces Lp[0 , 1] , 1< p< ∞
(Springer, 2019)
info:eu-repo/semantics/article,
Our aim in this paper is to attain a sharp asymptotic estimate for the greedy constant Cg[H(p), Lp] of the (normalized) Haar system H(p) in Lp[0 , 1] for 1 < p < ∞. We will show that the super-democracy constant of H(p) ...
Embeddability of ℓp and bases in Lipschitz free p-spaces for 0 < p ≤ 1
(Elsevier, 2020)
info:eu-repo/semantics/article,
Our goal in this paper is to continue the study initiated by the authors in of the geometry of the Lipschitz free p-spaces over quasimetric spaces for 0 < p ≤ 1, denoted Fp(M). Here we develop new techniques to show that, ...