A four-way conversion catalyst for treating a gasoline engine exhaust gas has a porous wall flow filter substrate with an inlet end, outlet end, substrate axial length extending between the inlet and outlet end, and passages defined by porous internal walls of the substrate, the passages having inlet passages with an open inlet and closed outlet, and outlet passages having a closed inlet and open outlet. The internal wall pores have a three-way conversion catalytic in-wall coating with an oxygen storage compound and a platinum group metal supported on a refractory metal oxide. On at least a portion of the internal wall surface defining the interface between the internal walls and the passages, the catalyst has a porous on-wall coating from the internal wall surface to the passage. The coating has porous oxidic compound and platinum group metal content of 0 to 0.001 wt. %, of the total coating weight.