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## Mixed means over balls and annuli and lower bounds for the operator norms of the maximal functions

Čižmešija, Aleksandra; Perić, Ivan
Mixed means over balls and annuli and lower bounds for the operator norms of the maximal functions // Journal of Mathematical Analysis and Applications, 291 (2004), 625-637 (međunarodna recenzija, članak, znanstveni)

Naslov
Mixed means over balls and annuli and lower bounds for the operator norms of the maximal functions

Autori
Čižmešija, Aleksandra ; Perić, Ivan

Izvornik
Journal of Mathematical Analysis and Applications (0022-247X) 291 (2004); 625-637

Ključne riječi
mixed means; integral means; balls and annuli; potential weights; Hardy's inequality; Hardy-Littlewood maximal function; spherical maximal function

Sažetak
We prove mixed-means inequalities for integral means of arbitrary real order, where one of the means is taken over the ball in R^n centered at x and of radius delta*x, delta>0. From this result we deduce the operator norm of the operator S_delta which averages a function |f| from L^p(R^n) over the same balls, introduced by M. Christ and L. Grafakos (Hardy type inequality). We also obtain the operator norm of the related geometric mean operator (Carleman type inequality). Moreover, we indicate analogous results for annuli and discuss estimations related to Hardy-Littlewood and spherical maximal functions.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Projekt / tema
0037119

Ustanove
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb

Profili: Aleksandra Čižmešija (autor) Ivan Perić (autor)

#### Citiraj ovu publikaciju

Čižmešija, Aleksandra; Perić, Ivan
Mixed means over balls and annuli and lower bounds for the operator norms of the maximal functions // Journal of Mathematical Analysis and Applications, 291 (2004), 625-637 (međunarodna recenzija, članak, znanstveni)
Čižmešija, A. & Perić, I. (2004) Mixed means over balls and annuli and lower bounds for the operator norms of the maximal functions. Journal of Mathematical Analysis and Applications, 291, 625-637.
@article{article, year = {2004}, pages = {625-637}, keywords = {mixed means, integral means, balls and annuli, potential weights, Hardy's inequality, Hardy-Littlewood maximal function, spherical maximal function}, journal = {Journal of Mathematical Analysis and Applications}, volume = {291}, issn = {0022-247X}, title = {Mixed means over balls and annuli and lower bounds for the operator norms of the maximal functions}, keyword = {mixed means, integral means, balls and annuli, potential weights, Hardy's inequality, Hardy-Littlewood maximal function, spherical maximal function} }

#### Časopis indeksira:

• Current Contents Connect (CCC)
• Web of Science Core Collection (WoSCC)
• Science Citation Index Expanded (SCI-EXP)
• SCI-EXP, SSCI i/ili A&HCI
• Scopus