The Paul Hanson Lighting Company began in the 1920's and as a collectible today as then. Their appeal lies in the quality of the materials- porcelains, high quality wood, marble, bronze and brasses. They were created using molds as well as cast metal in a lost wax process. This process is based on carving a form from wax and burying the wax form in sand. Then the bronze, or other metal, is then poured into the sand and the wax is burnt away with the metal filling the void left, thus making the casting. It is an expensive process reserved for art pieces.
The most collectible of Paul Hanson lamps are from the Hollywood Regency style and the Chinoiserie styles from the 1940's through 1960's. The style hallmarks include detailed pierced work, Mid-century modern geometric lines, and more traditional styles of retro-fitted porcelain vessel shapes with Asian inspired painting and classical lines in glass or brass.
Some of the marks of Paul Hanson include:

Paul Hanson sticker on the lamp base- image from 1st dibs

PH button on the lamp base- image from 1st dibs.

Paul Hanson mark on the base of a double dolphin lamp.- image from 1st dibs
Fantastic lamp forms include:
Square forms with pierce work, or lattice-
Above image from personal collection
Image from EBAY- pair of Chinoiserie lamp basesFrom EBAY- Stainless steel and Brass lamp base

From 1stdibs.com- clear cracked glass with brass spacers lamp base

From 1stdibs.com- Pottery Ball and brass spacer lamp base