English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Let $$L_k=-\Delta _k+V$$ L k = - Δ k + V be the Dunkl–Schrödinger operators, where $$\Delta _k=\sum _{j=1}^dT_j^2$$ Δ k = ∑ j = 1 d T j 2 is the Dunkl Laplace operator associated to the Dunkl operators $$T_j$$ T j on $$\mathbb {R}^d$$ R d and V is a nonnegative potential function. In the first part of this paper we introduce the Riesz transform $$R_j= T_j L_k^{-1/2}$$ R j = T j L k - 1 / 2 as a $$L^2$$ L 2 -bounded operator and we first prove that it is of weak type (1, 1) and then that it is bounded on $$L^p(\mathbb {R}^d,d\mu _k(x))$$ L p ( R d , d μ k ( x ) ) for $$1<p\le 2$$ 1 < p ≤ 2 . The second part is devoted to the $$L^p$$ L p smoothing of the semigroup generated by $$L_k$$ L k , when V belongs to the standard Kato class.

Semigroup and Riesz transform for the Dunkl–Schrödinger operators